{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting Started"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import scipy.stats\n",
    "import scipy.signal\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def change_plot_size(width, height, plt):\n",
    "    fig_size = plt.rcParams[\"figure.figsize\"]\n",
    "    fig_size[0] = width\n",
    "    fig_size[1] = height\n",
    "    plt.rcParams[\"figure.figsize\"] = fig_size\n",
    "\n",
    "change_plot_size(20, 6, plt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate an Idealized Bidirectional Arc Curve\n",
    "\n",
    "This generates a vector of a matrix profile indices that randomly point to different parts of the time series. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 5000\n",
    "\n",
    "mpi = np.random.randint(0, k, size=k)\n",
    "AC = np.zeros(k, dtype=np.int64)\n",
    "nnmark = np.zeros(k, dtype=np.int64)\n",
    "\n",
    "for i in range(k):\n",
    "    j = mpi[i]\n",
    "    nnmark[min(i, j)] = nnmark[min(i, j)] + 1\n",
    "    nnmark[max(i, j)] = nnmark[max(i, j)] - 1\n",
    "\n",
    "AC = np.cumsum(nnmark)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit a Beta Distribution to the Idealized Bidirectional Arc Curve\n",
    "\n",
    "Average the computed alpha and beta parameters across 1,000 iterations and by drawing 1,000 samples from a distribution that is sampled according to the unnormalized histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.99 1.99\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11b9eaab0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_iter = 1000\n",
    "params = np.empty((n_iter, 2))\n",
    "for i in range(n_iter):    \n",
    "    n_samples = 1000\n",
    "    hist_dist = scipy.stats.rv_histogram((AC, np.append(np.arange(k), k)))\n",
    "    data = hist_dist.rvs(size=n_samples)\n",
    "    a, b, c, d = scipy.stats.beta.fit(data, floc=0, fscale=k)\n",
    "\n",
    "    params[i, 0] = a\n",
    "    params[i, 1] = b\n",
    "\n",
    "a_mean = np.round(np.mean(params[:, 0]), 2)\n",
    "b_mean = np.round(np.mean(params[:, 1]), 2)\n",
    "print(a_mean, b_mean)\n",
    "\n",
    "ac = scipy.stats.beta.pdf(np.arange(k), a_mean, b_mean, loc=0, scale=k)\n",
    "slope, _, _, _ = np.linalg.lstsq(ac.reshape(-1,1), AC, rcond=None)\n",
    "\n",
    "plt.plot(np.arange(k), AC, color='red', lw=3)\n",
    "plt.plot(np.arange(k), ac*slope, lw=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate Idealized 1-Dimensional Arc Curve\n",
    "\n",
    "This generates a vector of a matrix profile indices that randomly point to some part of the time series ahead of its own position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 5000\n",
    "\n",
    "mpi = np.zeros(k, dtype=np.int64)\n",
    "mpi[:-1] = k\n",
    "for i in range(k-1):\n",
    "    mpi[i] = np.random.randint(i+1, k)\n",
    "AC_1D = np.zeros(k, dtype=np.int64)\n",
    "nnmark = np.zeros(k, dtype=np.int64)\n",
    "\n",
    "for i in range(k):\n",
    "    j = mpi[i]\n",
    "    nnmark[min(i, j)] = nnmark[min(i, j)] + 1\n",
    "    nnmark[max(i, j)] = nnmark[max(i, j)] - 1\n",
    "\n",
    "AC_1D = np.cumsum(nnmark)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit a Beta Distribution to the Idealized 1-Dimensional Arc Curve\n",
    "\n",
    "Average the computed alpha and beta parameters across 1,000 iterations and by drawing 1,000 samples from a distribution that is sampled according to the unnormalized histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha = 2.06, beta = 1.66\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11ba94860>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_iter = 1000\n",
    "params = np.empty((n_iter, 2))\n",
    "for i in range(n_iter):    \n",
    "    n_samples = 1000\n",
    "    hist_dist = scipy.stats.rv_histogram((AC_1D, np.append(np.arange(k), k)))\n",
    "    data = hist_dist.rvs(size=n_samples)\n",
    "    a, b, c, d = scipy.stats.beta.fit(data, floc=0, fscale=k)\n",
    "    \n",
    "    params[i, 0] = a\n",
    "    params[i, 1] = b\n",
    "\n",
    "a_mean = np.round(np.mean(params[:, 0]), 2)\n",
    "b_mean = np.round(np.mean(params[:, 1]), 2)\n",
    "print(f\"alpha = {a_mean}, beta = {b_mean}\")\n",
    "\n",
    "ac_1d = scipy.stats.beta.pdf(np.arange(k), a_mean, b_mean, loc=0, scale=k)\n",
    "slope, _, _, _ = np.linalg.lstsq(ac_1d.reshape(-1,1), AC_1D, rcond=None)    \n",
    "\n",
    "plt.plot(np.arange(k), AC_1D, color='red', lw=3)\n",
    "plt.plot(np.arange(k), ac_1d*slope, lw=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(1846)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(AC_1D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reproduce Michael Yeh's Matlab Example for the 1-Dimensional Arc Curve\n",
    "\n",
    "This is here for reference only and should not be used. The above approach is much faster for finding the the right alpha and beta values for a beta distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [None] * k\n",
    "for i in range(k):\n",
    "    x[i] = np.ones(AC_1D[i], dtype=np.int64) * i\n",
    "x = np.concatenate(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, b, c, d = scipy.stats.beta.fit(x/k)  # This takes a while"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha = 2.0686952775402663, beta = 1.6552807056956045\n"
     ]
    }
   ],
   "source": [
    "print(f\"alpha = {a}, beta = {b}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This takes a while\n",
    "y = scipy.stats.beta.rvs(a, b, size=x.shape[0])\n",
    "y = np.round(y * k).astype(np.int64)\n",
    "\n",
    "AC_1D_Yeh = np.zeros(k, dtype=np.int64)\n",
    "for i in range(k):\n",
    "    AC_1D_Yeh[i] = np.sum(y == i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "ac_1d_yeh = scipy.stats.beta.pdf(np.arange(k), a, b, loc=0, scale=k)\n",
    "slope, _, _, _ = np.linalg.lstsq(ac_1d_yeh.reshape(-1,1), AC_1D_Yeh, rcond=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11bb79e20>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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288X3d48y2PfC2lP45vaRuseXInRSUN0MlVqDCB8Xk30XMqShHyNj5gkREdHlicETIiIiIiKii6S1XYWNJ0owMdoXPkZ38FvS1HFXf31rO5oVKgR4OAqOu2/FMZwuqcf61GLkvTXXZL9xySihNd12lRpvbz5jsG3f2Uqb52oP/WyOeZ/sh5ujFA0dzdDlUgnevn6wwXj9rI3OxvMbT5bgrU2G8wWAW745jIUjQ03OIZNYDp4YZ+d0PlIo7Q+ePLP6JG4aFWaw7dejhSbjlh3INSiNde8PR3XNzz/Ylqnbbmumzq4M4Ybp+m799jD+MzcGvfQCVK+sT8fpEtNsGanea+bh1NUzRqPR6Mp37cmsQJFR4Km8QWF4ooscPVGq1Bjf0Zz98HNTzY67EBkxGoGG8URERHR5YdkuIiIiIiKii+StTWfw5G+pWPhVol3Hda69Dn55K0a/uQOVjQrBcZllDRbPYyYZw4C9ZaUsMS43pt+wPruiEX+mFBvs7wycAECeXkP67IpGfLA1AzXNplkRlub7y9EC5FQ0oqG1HXcvP4I/jxfBwUrmifHpOhe+FUqVxePOR5vK8KJKvccOeoGLCuNghBl3LTti07jXNp42CMgIBU4AbSZSflUzAMBFLtFtVyjVBq//2Ld22nRdaxpa27HzTBnaLASsNBqN2e8D/fl1in9jh+A5jFk7p630z6xi9ISIiOiyxOAJERERERHRRbL5VCkAwwbcQlraVHji1xTdY+O11zSBXhqA9cCHLT1P7O3tYYn+wrxGo0FTW1dwxNxz6KRUa/D7sUIczavGnI/24eOdWYIlr6w95ynv78HL69Kx80w5HvslxWrmifGCukqjgUKp6lbmiS3+OlkC4yk5OXQFKPTLj5UY9RDpCc+uNn1NhSzdnwMAcJJ1ze3rvTkWj0ktqMXmUyVm9x/MqkTEMxvxoV52DaDNvLl7+VG8vy3D7LHvb83EyNe247ejBWbHbEkrtTg/oa+cR34+bvEYWxmWQ1P3WN8iIiIiungYPCEiIiIiIrpIbK0O9OWebKxOLjK7v7tFhowXizUaDTQaDbLKG3VZIbZmnqxPNb8o3qld2XWue74/ikEvb7V5rsfO1eCp31Jx/ZeJusBFtUDDdFvm+0dyV6ksa/Ej4/0v/HkKw17dhqpG25u166tpasOjq1LM7n9gZTIkRl8Y+gEK/cbtFyJ4Yis3R225Lv2X+wOjoIeQ+1cko7xBO2/jr9tbvj0MAPhox1mD7YdyqgEAvx7pCozszazQlWoDgE93ZQEAXlqXZvbaT/yaanFu56qakVXeaLDtYHaVxWM6CWWtGA7o+vCGLxMx8d3dLN9FRER0mWHwhIiIiIiIqJs0Gg32n61EWb12cbhdpRZsuN3J1qBHYY1w03LdeQRO1KyX1WGO0ILv57uzMe2DPXji1xQczKpEu8r8Cm95fSve35qBwppmrDluPrjTSaHqKnW144z1PhzdYW+ZsQorZZl2nClHeb1hkKK5TYXNVrIYzNEP3JhzJK/G4LFUIvyV8nNSfrfm0BPcHLUtU23JXjLW2b/F3t4izW3ar5+Suhbc/l0SrvrsAADg2Llq3RjjwJO9pn2wx2Sbteyrf/9+AuPe3mXxe934y7KotgW1Ld0LwBEREdGlweAJERERERFRN+3OqMBtSw8j4U1tP4WZH+7FkFe26u60N2br4rHSSnMSkUAYRj9DwRyhQMO7W7Slkf5MKcYt3x7GgSzh5vBJudW494ej+GRnFsa9vcvqtQBY7FnRU+ztJ7E3s8Li/tMl9Rgl0B9Dvx+LPfQbrJuTmGOY7ZBjpazbpdD5OnenJc7pknpUNioMgg1H8qotHKGlUKqhUKpQXt8V8FKpNfjX7yd0j4W+pewNp5TUGQYrpwsEVPT9crQARbUtWHHonMH2gupmfLzjLPKrmqERKAom9H1LREREf18MnhAREREREXXT/o5AQ+eCck6ldtF7/1nTAITVMj96lEbZHxpoDJqtiwXWYIW27T9biRS9Uke2LHybC54U1jQjtbDO+gn0dJbZ6mw2fiFcrF4SDa3mswwscZFLe3gml0bn15+6G9GTR1elYORr2w223fBlok3HHsiqRKleJtDpknrIxF1LGZKOL3x7vr+MlRllGuXZ+PVqHHR5+vcT+GBbJp7+I1Xwe00ooAIAn+/Ows1fH0JruzbT5r0tGbjjuyT2SSEiIrrErox3cURERERERBdIQXUzPt+djdGRXpgW4w+JWATHjp4U5sorGTtRWItFS5MslvnRZ1w2SKMxyrAwuuxnu7Lw3lbD5tpl9a24bam2p0TeW3O15zG6jgbaO/cNTm3mKXUn4+BMaQNe23AaSTZkGXTXN/tyL9i59XWWnrKLRgOVog3ydgUkGjWkahUkahWkajVEGu3nWKN7wUXQiABNxydXIxJBo7dfAxGUYgmUEinaJFJoRBf3Xsiz5Y04nl/TrbJdtmhTquEgNX1Ody8/avB43if7MSK8l+5xu0qD59ecRKCHY7evXVpnWsqtrrkdHs6Ws4ZWHMrHk9Oj0cvFAUBXBtGhnGrBYI5+ULSqUQFvVzkA4J3N2u/dP5ILcWt8uK6fy2sbTyO3sgmvXzMQIb2cLc5Fo9GguqlNd04iIiI6fwyeEBERERERWTD+HW2Jqs5+E04yCdJfnQmRSGRwB7y+k0V1uGZYsK5M14tr02wOnACAUiBSYa63h0aj0ZXe0rfjdFePEaVKjW/35wqWrJJJxAbltcRmoicqK6XEhDQplBc0cGIXjQZyVTtc2lrg0tYC17ZmOLe1wrXjsUtbM1zbWuDc1grn9lbIlW1wVLZBrmyHXNWm99hwW+djmVqpC4xI1CpINGpINGrgHWD+BXg6KpEY7RIp2sUSKMXSjo+1/yvFErRLpFBIZWiVytEik6NZ5ohWmRwtHY9bpHLtY71tzQ5OaHRwRr3cGQ1yFzTKndEgd0a7RIa1KcVYm1J8AZ6JVnObEquOFOPFteYbwHdy1cvmaVQosfLw+fWCEepLM+K1bTj7+myrpfY+3nkWL80fgPTieoPtQjGm9JKuMSNe247n5vTHkglRum3NCpXB+OUH8wAAz64+iR8Xx1ucxwtrT2HFoXx8c/tITI/1tziWiIiIbMPgCRERERERkR1a2lVQqjWQSUS6kkHGlh3Iw4R+vpgc7QcAqGgwvbO9pqlNd8e6vrrmdpTUGZYR0sCwUbcIImRXNCKztAEbTpYIzuG5NSd1H9e2tOOtTWdMxjyt1ztCd24za8X//uOk8A4LbGkqbw+xWgV3RRM8Wht1/zxbGuChaIJ758etjfBQdH3spmjSBUhkapX1i1wmJBo1JMo2dD/fwnatUgc0yJ1RL3dBg9wZjQ7a4Eq93AU1Tm6odXJHtZM7ap3cUO3sjhon7b9aR1eoxRKbrtHcprIpcAIA56oufE8YpVqDysY2bDhRjJOFdbh9TASGhnqajFt2IA/3jI/EnI/3GWzPE5jjPqNyfm/8dQajI711j8317zH+eSBkxSFtAOm9LRkMnhAREfUQBk+IiIiIiOiyVd3UBi+BAMSFplJrIJMAMr2yXca9IDaeKMHkaD+cKqpDUW2L8Smw6VQpbokPM9k+5NWtphfUaAyyUQ7nVuF/28/aPN9pVhpg6/s5qcDmsdacsNIjRaRRw721CT7NtfBuroNXcx18muvg3aR97N3c+b/2n2dLA8Rm+kbQhePYkXXj21Rr13FqiFDv6KILrFQ5e6DCpZf2n6sXKlw8UeHSC+WuXigsrrL5vLb2JDlfT/2Wij0d2Vqrjxfpyt8Zm9iRnaZv0dIkm66x4NMDuo/VGo3ZDDNbdQY/04rrsD29HPdNjNSVGdSnUmvw5Z5sxPf2wsgIr/O6JhER0ZWKwRMiIiIiIrosfbsvB69tPI3/zI3BPeMjL+q1lWoNlu7PxXtbM3Xbnvo91WBM503k61KFSx09t+YkvFwcEN/bC69uSMcNI0IQr3cXujH94Iw9gROgm/06zoNIo4Z3cx38G6vh11gN/4Yq+DdWdzzWfuzXVAOv5rorKhuEDImhgWdrIzxbG4EaK4O/BE7IXVDu0gsVrtoAS5mrF0rcfFHs7oNid1+UuPmi0sXDar8XDYBigYClvfYIlLlrUihNtgmV2euOopoWTBAIxNjWWcnQ3I/3AwBalSr8e1Z/k/2rkwt15f7MBYW6o12lxonCOgwJ8YBUcnH78hAREfU0Bk+IiIiIiOhvrU2pRkldC8K9XQy2v7bxtO7/kF7OmDUw4KLNSaXS4L8b0g22rU42LFHV3KbEwq8ScTjXfM+P+1ccw40jQ7DmeBHWHC/ChH6+guM0MN/z5GITq1XwbapBcF0FguvLEVxfgcCGCm1wpEEbLPFrqv7bB0XUEKHJwRFNDk5ocnBGo4NTx8eOaJY5oVXqAIXUQdc3RCGVQSExeix1QKvUAW0SGdqkMqhFYijFEqjEEm1zd5EEanHnNjGUIu0+lVgMdUcAQKTRQNSRTaP92HgbAGgg0mgg1aggUykhVangoG6HVKV9LFMrIVWrIFO1Q6buGKNWQq5sg1O7Ak5KBZzaFXDU+9ipXQHHjo+d21t1/7spmuGmaLoknz93RRPcFU3oU23ag6STQiJFmas3Stx9UeTuixI3H5S4+6LYzQeFHn4o8AiASq3BmLd2XpA5vrYx3fqgbjLXu8We73zjHi2pBbWC4/TLih07V4M2pRoJUeaDt52O5lXjr5OleGpmPzg7mC4pvbg2DT8n5ePusb3x4vxYO2ZORET098PgCRERERER2eVwThVCvJwR7Ol0Ua73fyuOYceZcnx/9yhMNBNcuH/FMfx0TzzG9PGx6ZyNCiWO5FZjbB8fOEiF745uV6nx1Z5swX0KlfWF5U2nSm2ai34JIqGG7oC2/NWsARcnOOTY3oqg+koE15cjqL4CwXXlCG7Q/h9UX4GAhio4qE3vvr/YFBIp6h1dUevohjpHV9Q5uqLW0RX1uo+7tjfKndEkMwyUtMjk5hu8/NNpNHBUKuCmaIGboqnjX3NH/5hmuHd83NlzpldLA3q11COwvRFODbVwazv/rA9z5ColwurKEFZXZnZMwzJvzHH2xblegSjwCEC+ZwDyPf2R7xmAclcvq5krluw6I/w9eimsSy3G2uNF+GDhUN0246/ozqyYU0V1kEpE6B/gDgCQirteg+u+OAgAWLE4Hsn5NbhvYiTk0q5SXyV1LcirbEZClDeu/zIRACCTivDs7BiTOf2cpA0AfXcgl8ETIiK67DF4QkRERERENjtZWIeFXx8C0LOlXizZcaYcAPDVnmyzwRMAOFFUJxg8qWxU4LUN6bh5VJiuLNb/rTiGfWcr4SgTI/WlGUgrrsfAIA+DQMqPiecMynLpa2nrubvyNWaaROv7/VghnpzRr6cuCJ/mWoTVlCK8tgRhtaUIqy1BeK32sb19LXpKvYMzqlw8UO3kgSoXT1Q6e6DK2RPVzu6octY+rnb2QK2jG2qdXNEqZfBD3/EXpmPYf7f1zMlEIrTKHNEqc8SwUf2xNd18oELfuD4+2J9VCQdlOzxaG+DVUo9eLfXo1VwPr5Z6eDfXwbepBr5NNfBrrIZvUy38GqshV/VsWTm32iqMqK3CiOIzJvsUEhkKPLSBlFyvYOR4BSPHKwTZXsEod/Wy+jVVWm+9efvF8sjPxwEAn+3K0m0znn5SbjVOFNbqeqtkvDYLcqnEoF9Tp9uWHgYAOEjFuH9ilG57wpvaLJ7f7k/Qbcup0GauZJQ24EheNW4ZFQaxmN+PRER0ZWHwhIiIiIiIbJZSYK1xgbbMVll9K0K9nHv02pWNCov7zcUgXl6Xhg0nSvBnSrEu4LPvbCUAoLVdjbFv7UJlowLXjwjBezcM0R33+W7hrBMAaFJYD564yaVoEOiPYOxInvXXFNA+D1uJ1SoE11cgoqYY4bWlCKsp0QuUlMKl/eIsAKtEYlS4eKLM1Rvlrl4o6/hX38sX5+Ta5uHVHUERhdShx6//2/0JWJ1ciJ+TCkz2rVgcr1ssvhL0cjn/129MlDcOZnc1bl9+VxxWHBIuJSVE3hF8bJPKtA3hXW1oRK7RwF3RpBdU0f7v21iNgMYqBNVXIKi+Ev6NVT1SSkyuakef6kJtabCcowb7GhyckOMV0hFQ0QZVcryDkdsrCK0yR4O+Q38n1U1tuo9Vag3+OGZY9ky/KX15vQKhXs4W+5FklDYIbk8+1/WzqvPn7cz/7QUAOEjEuDEu1O65ExER/Z0xeEJERERERDYzV+JK301fJyI5v9amMlrVTW3wsnHRt8ZK0/O3N59BRmk9/nfTMIPtnXdIm9MZlPn9WKFB8MRSsKal3XpQpKeTIrakmd79797aiKiqQkRWFyGyuuv/iJqSHr+b35hCIkORuy+KO/6VuPl0BEi8dUGSShdPqMUSk2PdHKVoaL3wpb/6+rnizWsHY/G4SEz7YI9u+3/mxmBcXx8MDHbHqaJ6u86Z88YcRD73V09P1aIPFw7BjtPl2HCipNvnGBzigROFdRbHLIwL1QVPsl6fDalEjBWHztl8DbmsG+WwRCLUd5Rby/YOxdI7RmLx90dNhonVKvg01Xb02KlEYH0FgnT/VyC4vuK8s6bc2lowpPQshpSeNdlX4OEPzcmReLraCRk+4cj0DUe2VyjapLLzumZPO1PagCd/SzW7/8/jRXh4al9ILWSJmPvZ9eYm00yeTieL6mwKntQ1t8PVUQoJs1SIiOgywOAJERERERHZzJbgSXJ+LQDgl6MFFoMnH2zLxMc7zuLDhUNwzbAQq+e1pWH6nynFeGZ2DDadKsENI0PhKpdCbUNZLHs121C2y5YxtpCoVQirLUVkdaFJoMSn2fJi+PmocXRDkYcfijsac2v/dTz28EOVswc0IjGW3jESTwssdltiy+eyJ8g67q43XqcVd6wOi0w6RFh2S3zPlCZatWQ0buoof2cLfzdHfHrLcGw4sdHiuCUTIvH13hyT7W9dOwizBwZiyKtbbb5mZ2aCPd8+DmayGYwzWiwZFOwhuF0tlqDczRvlbt44LrD/5lGhWHPgLEJryxBWV6rLsgqtLUVYxzZHZZvAkbYJrSsD/tqIB/S2KUVi5HoF64Ipnf+f8wwQDBr+Hby/LRMPT+2r+94Q0vn9Ud/ajhs7epyY0hg90uAnMw3vOxVUN2P8O7swPMwTqx8Ya9e8iYiILgUGT4iIiIiIyGYOkq4FQZVac153D3+8Q3t39/NrTtkUPFGq1FiXWozdGeWY2t/f7LiFXyfiXFUzThXV45WrBuCMmRI0luiXwRGSVmw9W0FpZ4BApFEjtLYM0ZXn0LcyH/0qzyG64hwiqwshV/V8lkabWIqCjiba5zwDke8ZiHO9ApDvEYAiDz80OzjZdB5bAmom11aq7T6mO6QdfR2Mv047H9qTHSQRi/DGNYN0x6s1wPUjQpBeXI/evi7YaEdWiEwiwtg+3jiQZVtAwdaAzXNzYnAop8okw2TGgAB4OFvPkJALfC71g4/j+/roSt4JMfe1MH9IkM3BEz93R6x5YAyu+fygTeM7xUV4Icp3GF7beBpnfcMN9vm7y1Fe1wKfplqEdfT2Ca8pQVRHILJ3dTGclJbLAgqRatToW1WAvlUFQMZ+3fZWqQMyfMKR5h+FNP9IpPlH4bRvBBQyud3XAICy+lb8ebwIcwYFCr7G3fkpbCl4Iun4xlh5KN/mn58pBbUmJd4Kqpvh7+6om/O61GIAXQF2IiKivzsGT4iIiIiIyGb6C3cKpQrODub/pLB1Qc/WLIR2lUbXIHl1cpHZceeqmgEA29JL0a7q3iL982tOWtz/loXyNVZpNAiur0C/ynMd//LRr+Ic+lQVdmsB15J6uQvyemkDI/me/gZBklJXb5vvjvdxlZstY2Yu28ASewNL3SUTd2aeGAVPxJ2ZJ3acS6/B9pHnp6GkrhUDO7Ikvt2XY1fwRCoW49vb4xDz4mabxtvzdSwSiAhJbIwSTYr2w4AgdwwJ9dRt0/9UXTMs2GLwRC4V/nqyN8Y6LKyXfQcAcJJJzAYEHKRiaERiXR+WYyGxBvtFGjUCGyoNM7uqihBZXYTghgq75+KobDMp/6USiZHlHaINqPhFIr0jsFLv6Gr1fA2tSjz2SwqKaltw19gIHMyqwvoTxXbPS5+lsl0d3zZQWvi602iAKr2fCSW1pn2Uxr+zC0NCPbH2wbEdx/w9e8YQERGZw+AJERERERHZTD940tLWFTxZl1qMXs4yjO/ra/c59e9sVyhVZhdgW9rtK4OlVGt0dzp3uubzA/jP3Bizx2SVN+DeH44ht9JynxRbObe1oH9FHmLLcxFTnoPYslz0rcqHa1tLj5wfANrFEuR7BnQ1uNZrdl3l7NEjzVdWLYnHRzuysD7VdMG2O5knMokI7arzW0h989pBeHa15SBXZ5DEOHNDF0wReG1GhvfCUb3G2J30AxDernJ4u3ZlERgvRD8yta8us0qITCKGk4Ph1/m71w/Gv34/IThe0X5+mTpiGz9FjjIJNj4y3mCb/venpSbjgPDXwoxYf7vLowFA/wA3u7LGHGUSs5lw1gJ8GpEYxe5+KHb3w77eww32ObW1IrKmCH0q8xHdkQ0WXXEOIfXlNs8NACQaNaIr8xFdmY9r03bptud7+ONkQB+kBvZDamA/nAzoYzbra2t6GcrqW/FDou19aIQkZlfh6T+Ev9aArgCcpYwnDYA3/uoKItc0C2frpRbUdh3D2AkREV1mGDwhIiIiIiKb6d853NpReimjtEGXEXLb6DDdfuM74Otb23HP8qOYOzgQd4yJ0G3vzDz5ak823tx0BquWjMboSG+T69lLKbA4fzy/Ftd9Ya6Gv7aEWLcCJxoN/BurEFuei9iyHMSU5yK2PAcRNSUQo2dWDCudPYwCJNr/8z0DoJRc2D/tpGIxHpgUJRg8kdq6Mt/Bx1WOu8dF4J3NGWbHJD03FaPe2GF2/7bHJ8DHVW41eNLJfM8TQ78sGY3vE/PMnMP8QrJxUOGJ6f2sBE9MzzUp2g+3xodhZUffiGkx/th+ugwAdIEWJ5nEJIg4Jsobw/UyNYRmaRxUcHGQoMmoJ8+o3l5m56ubt5UUEqHgyXs3DsGWU6W6x3ERvXAkzzA4NXtgADbpjQGAL28bgUnv7bY6p05SichsNkXLefQfanFw7Ci/FWWw3VXRbFBer1/lOURXnrO7aX1YXRnC6sowN+MAAG2GSqZPGFI6gimpQf2Q6RMOlViC2ua28w6cAMDN31jut9MZKLT0Na/RaFBa3xUEtiWZjLETIiK63DB4QkRERERENtOPZbR2LOLmVDTqtunXvDdedvvhYB6S8qqRlFdtEDzpXHR7s6MU1jN/nMDuf03G13uz8cXu7G7PtV2ttjvD4XButdUxErUKUVUFGKAXJIktz4VXi/U+KLaodnJHQVAkUt2DkekThkzfcGT6hKHWyd3uc43v6wNFuxpJedaflyWWetvYGTvB0f9Mw69HCyyO8XN3tLi/r78bGlrbTbaHeTkjv7rZZLtx2SpXR+2fwsZrw/GR3mYXpyUCAQ/dPjvrUhmXl5rYzxe+bnKDxeVvbh+BlYfzkV5Sj4SOYOKmR8ebBBR+une01esZL4K7yKUGwZPn5vTHdcOF+w7pf89byzwR6pni7igzuP6b1w7CtA/2GoyZ0t8Pm06VGgQ/InxcLF7LmKJdfV49mOzVKHfG8eD+OB7c32C7V3Md+pfnYkBZDgaUZ2NgaTYiq4tsDqJKNGrEVOQhpiIPN5/YCgBolslx0l+bnZISFI2jwTEod/Pu8efU6cdD5/DKggGw9OkuqGmBj6uDXedVM/WEiIguM3YHT/bu3Yt3330Xx44dQ0lJCdasWYOrr75at1+ovioAvPPOO/jXv/4FAJg0aRL27NljsH/hwoVYtWqV7nFNTQ0eeeQRrFu3DgCwYMECfPLJJ/D09LR3ykRERERE1A1VjQrc/M0hXDs8BPdP1N51rb/41ZnZ0aq07a7u97Zm2jSuoVUJjUZjUBKmOzQanHdpKJFGjcjqIgwqzcLgkrMYVJqFAeXZcG4//94k9XIXZPiE46xPGDJ9wpDhq/240tkTQ8J6GZS76a77J0bhf9tte90tkYhFZkvudKckk7oHep7oByDWPjgWgZ6O8HWV445lR7A307BPhf7fqf0D3DBnYIB2u96YL28bAZONeiz1DbH3FehsZH/PuN5YfbwI714/GIBhoEIkEuG20YaNz20JKNw9rjce+fk4RKKu8xkHFYxf/SUTomCOYdkuy8/U+DWa2t8PADBrYAA+2JaJkRG9BPuSzBgQAB83OfoHuBlsl0vFUCjNlyxbesdILP7+KADAzVGKBoVpQA0wX35q5gB/bEkrM/+EuqHO1RMHnYfiYMRQ3TantlbEVORiQFm2NqhSlo1+lecgVyltOqdzuwLxhWmIL0zTbcv38MeRkFgcC4nFkYpYiHxCoRHZX0LPnF0Z5RYzT7LKG+HlbD1bSV+b0edSrdbg5yP5GBnuhWijzz0REdHfgd3Bk6amJgwZMgR33XUXrrvuOpP9JSWGTfI2bdqExYsXm4y999578eqrr+oeOzkZ1vS85ZZbUFhYiM2btQ30lixZgkWLFmH9+vX2TpmIiIiIiLrh893ZyCxrxFubzuiCJ/rN3TubWLfa0I/hVFGdzdetamrDU7+Zr8d/oYg0aoTXlGBwaRYGlZ7F4NIsDCjLPu/+JEqRGDleIUj37410v0ic8Y1Ahm84yly9zfYjcZIZLoKG9HJCYY398xCLRBYXQIU8M7s/3tpkGLiSikWI8rMtE2Df05Ox8KtEFNeZNpD+9yztXfr6DeODPZ1QVGv63N6+bhC+2puDnAptGbUR4b1w7FwNBnU0adfPUvB1k8PPTZutIhSY0Q8efLVohC6DQj+oMksgoKLPUv8Ha6+xl4sD7hoTgfe3aQNZnQGE/8yLxXNzYnTnvmd8b/yclI+rhwZZPJ8lC4YEITbQHeeqmnSBBeOghj3l8PSH+ur1eemU9spMDHhpCwAgxMvw7/pv7xgJQJvpsu/pyRCLRYKfa4lYhMnRfibbk56bhgZFO8a9vctkH6AtE/bRTUNxprQBo3p7Yf2JEsFx5phrMH8+Vv/fGFz12QGDbS0OjkgOjkFycFe/JZmqHX0rCzCwNAtDSjMxpOQs+pfnQqqxrb9NZ7mv6zr6p9Q6uuJYcAyOhsTiaHAMTgT2g0JqX2aIvkaF0momj1Jtey+er/Zk43OjTMI/kgvx/JpTAIDcN+eYvRmXiIjoUrE7eDJ79mzMnj3b7P6AgACDx2vXrsXkyZMRGRlpsN3Z2dlkbKfTp09j8+bNOHToEOLj4wEA33zzDRISEpCRkYHo6Gh7p01ERERERHZqFWjQrr8u3RU8Ec48KdRbJG1UGN5hfeyc5TJSfyQX2jrNbguor8Sw4jMYUpKJQWVZGFSaDXfF+TWKb3Bwwmk/bZAk3S8Sp/16I9MnDAqZ4aLzsrvicNeyI2bP4yo3/FPtkSl9LTZ4NkciFuGVqwZg8fKjuHNMBF7/67TF8YEejrh/YpRJ8EQiFkEuleDrRSOw5MdjZo9/5/rBCPVyRpi3s0HwxM1RisPPTYWzg/Z5TenISIj0cUE/fzfBBfWFcWFYGBeGTSdLIJWIMSK8F34/VoCrhwUD0JaQempGPzS1qRDk2bVorxIInuivAetnyggFA8wFQixlngwJ9dR9nPjsFIN9swYE4KObhyK1oCuAqL9orx+UifJ1xelXZ8FRdn6L+n38XFGs95oaB37sqZ6k0ctTEcp8cZJ1Nb53k8swf0iQrjeO/mJ45xzaBTJJzL22Hs4yeDjLMDTUEykCmVgSsQhXDQ3GVR2PzfU8MRcksdZIvjv6+duWQdEukSHdPxLp/pH4dcgMAIBjeysGlOVgaHEGhpZkYkhJJsLqbMuM8WxtxNTsI5iarf25opBIcTKgLw6FDUJi2GAcC+6PVpnlcnj61BqN1aBgcn6tzed7c5NpJuGJwq7viQnv7sKmRyeY/OwjIiK6lC7ob6WysjJs3LgR33//vcm+lStXYsWKFfD398fs2bPx0ksvwc1N+yYjMTERHh4eusAJAIwePRoeHh44ePCgYPBEoVBAoehKna+v75l6w0RERERE/1RClZX071jvLIllLvMkKbcaCqUKcqnEZJ+lwMGFIG9XYGBZNoYXncGw4jMYVpyBwMaq8zpnobsvTncESTqzSgo9/KyWzpkW4494K825HaRivHHNIDy3RtsQ/foRIRaDJ0NDPdHLWYZdGYblqiRiEfoHuOPAM1N057n9uyQ0tSl1GR36zC2Wdi6CO8pMP5cGh3R8eegvzqe+OANymdjg2CBPJyS/MB2ucike+inZ7PMCgNmDAnUfG5eXemhKX5Pxd4wJR2JOFcb18dFt0w8e6AcDXrlqAJralFikVx7L3Hrxg5PNl7aKDnDD29cNgggiBHoYZl84O0ggl0rg59YVqLEUiOlsDn8h9PVzxdnyRswYEIDqJgW2pJXp+qmYo7+YLbSwrf/aqjQaRFopLRbq5WyyzVrCwbI743AkrxqvrE83CLQZB0XMZUqYC5KEeZvOxVZfLRqB+wQCidZKmwHA5sfGY9b/9plsb5U54lhHKa5O3k21GFx6FkOLMzGs+AyGFmfAvc20r48xuUqJkUWnMbLoNB5K/BVtYimOB0XjUNggHAobjOTg/hYzU1Rqy9lW58s4yFlQ3YK1KUW4Nb7re/FIXjV+OpyP5+fGwEcg0GnN78cKcbKwFi/NH3BBnwsREV25Lmjw5Pvvv4ebmxuuvfZag+233norevfujYCAAJw6dQrPPvssUlNTsW3bNgBAaWkp/PxMU3b9/PxQWloqeK0333wTr7zySs8/CSIiIiKiK1xhTTNSC+owe2CA1QUmlca0bFeLmcwTABjw4hYsuysOO06XG2yvbzXMRDlXdX4ZHwY0GoTVluqCJMOKMxBbngOZ2rbeLEJKXL1xMrAvTgT0wcmAvjgZ0AfVzh7dOtfIiF6QWumy7iARGyzCWvu89PN3RUWDaR8W48XkXi4OWPfQWADA4Fe2osHo82BuWp19L4SCK/qBkuHhnibbPJxlguf0cnEwOHdPmTUwENufmIAwr65FfHPBCn93R/y4ON5gm9DIbY9PQB8/V4vXXRgXJri9MxgS0ssJwZ5OkMvEcHPs/p/in986HA+s1AacPlw4xK5jf14yGjtPl2PekEAo1RpM7V+KmQOEK0J0emn+AJTWt2LxuN7dnrM+oQCHtfJQvVwcMGNAAN4wypwyzjQxl3niINDIHji/sl3mXjdzc9DXP8Dd5utUuXhiV1QcdkXFAQDEahX6VeZjZGE64grTMaIoHSH1FVbOAjiolbq+KY8eXAWFRIbk4P5IDBuMxLBBSA2MRpu063tVrdF0o5uRMKEycZ2/P/QZB+xv+DIRgDa78YvOnkR6Vh4+h7XHi/HN7SMFf8489VsqAGBcX19Mj/XvztSJiOgf7oIGT7777jvceuutcHQ0TA299957dR8PHDgQffv2xciRI5GcnIzhw4cDEG48r9FozNbAfPbZZ/HEE0/oHtfX1yM0NLQnngYRERERkU00Gg3qWtrh6dz9OvOXQmc/gfdvGILrRoTo7TFd8BIq26WwEDxRqjVYtDTJ6hwmvrvbprkKcWprxdCSTAwvOq0LmHi3dD8TvcLFEyc6AiSd/1e42tcY2Rr9BdY7EsKhVGuw8nC+bptMIrZpEbbTM7NjdAuF5q7TqfNvqlERXthxxjCoZbZ8kpN2YdJcibak56eivF6BPn7aagL/NzkKScuqsWCI9d4dPdA73kTnPDrpB32sNbg3/ptzWowf+tpYiklIZ1krqUSM3f+apC2HdB53wc8e2LVoL9QnpJPQp9LHVY4b47r+Ttb/2JxQL2dseHi8xTE3jwpDakEtJkX7Iq3Y/u89W/vyGH9uLGWe6Jf6Mhc8sRa0MTY4xANXDw3GKAuZYyKRCPMGB2KDXv8Vkci+UmmWqMUSnPHrjTN+vbFi+FwAQGB9BUYWpmNkUTpGFp5G/4o8SKz0TpGr2pGQfxIJ+drsthapHIfCBmJfxHDs7T0MT/+mQUxQ9wLExob/d5vJNqXAN765XjzZFY2C2zv7pXy1NxtPd/RTElLb3GbLNImIiExcsODJvn37kJGRgV9++cXq2OHDh0Mmk+Hs2bMYPnw4AgICUFZmWtezoqIC/v7CdwvI5XLI5fancRIRERER9ZSnfjuBP5IL8fO9o5EQZbkUzqXSrlIjrbgeA4PcdU2zOyXmVBkET4R6AQuX7ep+Rkd3eDXXIa4wTXfn9YCy7G5nldTLXZAS2A8pgf10mSWWGrn3FP3F80EhniisMSzDU1zXAn93w5vQJGKRYD+P6bH+8HJxEAwJWFqUFsr4EFrUT3lxum6RemwfH0yO9kVClDfe+Kurh4Gfm6OuYTugXdRPen4qfFys/41mT/Py7rLn06k/9Mjz0+Dtcn7BUP2F9p5oUC4SibDp0fFobVdZDNSG9up+SSpLNjw8DvM+2W+w7c1rB3U96Mbn09YYRrS/G3Iru7LUjEtk6QdDpsX4dQVPzLzulsqnCRGJRLjbhgycT28ZDg2SsbEjgCKCaSh6UrQvdmdYzxixRYm7L9bHTkTquNl4qboZropmDC86jdEFJ5Fw7iQGlZ612ojeSanA5JxjmJyjLUVW4uqNfb2HYW/v4TgQPgQ13cy0A4Ca5naTbUqhzBO1BsfO1eDJX1Pw4vyu0mVCP/dS9XrgnC6px2OrjuPByX3OK9BJRERk7IIFT5YuXYoRI0ZgyBDracRpaWlob29HYKC2lm1CQgLq6uqQlJSEUaNGAQAOHz6Muro6jBkz5kJNmYiIiIjovHQ2Of9019mLFjw5WViHNceL8Oi0vrrsAAD4MTEPEIkMejkAwEvr0vDT4XzcO743np8ba7Avv7oZSpVaF1T55WiBbp9Go8GH288io7TrrnKlSg2NRoM/U4ovwDPTXRjhtSWIK0zXBUuiqrvXTF4lEiPTJwzHg/rjeFA0koP7I8cr2GqPEnuFejnh/olRuruirREB8Daq538gqworFsfjgUlRiA7QLgZue3wCpry/RzdmwZAgjO3jresJIrQObOnO+tvHRJj2SDE6yfi+PgYL9E4OEiy7axTUao1B8ESIfjDFEpXRuujI8F42HWcP/dfBasksvZfA1637N+htf2IC0orrL0i5oJhA62WfInxcsPSOkSZfW+drYLAH+vm7IrOsEZOjfXvknOYqTBh7/ZqB0ECDLWnamy0tZWfp91YRyjxZMCTIYlBtVG8vJOVWG260IzBkkO0kkHry9aKRuOeHo9ib2TMBFAAYGOyON68dhFu/PYy9kSOwN1Jb6spV0YyRhWkdmSYnMKAsx2pmSmBjFW48uR03ntwONUQ4GdBHF0w5HhSNdolwOT5btRt/40MbYLpzWRIaWpW4e/lR3Xah4MlVnx3Qfdz5c+xAdhWOPD/tvOZFRESkz+7gSWNjI7KysnSPc3NzkZKSAi8vL4SFaWu81tfX47fffsP7779vcnx2djZWrlyJOXPmwMfHB+np6XjyyScxbNgwjB2rrb0bExODWbNm4d5778VXX30FAFiyZAnmzZsn2CyeiIiIiOjvRChj40KZ/6n2DvBGRTveuV5741JdSzteWJsGADiaV41b48MR0ssJQZ5O+KmjNNQ3+3Lx/NxYLDuQqztXUm41Br68BQmR3nhD/05yADvPlOPjHWcNtrWp1Lj3h6OoazG9q7i7JGoVYspzDTJL/JpqunWuCmdPpARF43hQNI4H9ceJgD5okl+Yu/H17Xt6iu6Od1uIRMDCkaH4cne2rhl2L2cZRCKRQSmaSF/DnhteLg5GfTbs6yUxOdoP6x8ap/saAoBhYZ4GYwaYKdvTk82X9TNPfrs/AbE2BAbsJZOI8e3tI9GmUqOXlUwSW0tIWdPHz82kfNjFNjXmwvR5+HFxPP48XoQbR5qW/bqQeUTernK8fd1gbEnTloEyDrokRHrjprhQjI70hrND13LHkgmR2NMRpLgjIRxzBgViSKgnfk7KhzkvzI01+N4A7Htu+t8iQl9RDlIx+vi6CgZP9Pva2MP4d8+HC4fg8V9S0Sh3xu6oOOzu6Jvi3tqIUQVpSMg/gYT8E4gtzxU4WxcxNBhSehZDSs/iocRf0ejghH0Rw7AzKg67okai0sX+gKdQQKSmqQ1NCqXpWBuDVkJ9nwDbg3NERETG7A6eHD16FJMnT9Y97uwzcscdd2D58uUAgFWrVkGj0eDmm282Od7BwQE7duzARx99hMbGRoSGhmLu3Ll46aWXIJFIdONWrlyJRx55BDNmzAAALFiwAJ9++qm90yUiIiIiuuh6ugG2LdJLujJC2pRdK2hrU4qxNqUYzg4SpL86y+S4V9anGzxubVdjV0YFHv8lxWC7fqmcTi+uTTvvwIlErcKAsmyM7rgjemRhOtzaWuw+j1IkRpp/FJKD++N4UH8kB0Wj0MP/gpffMseeckAikXYh9aObhuL6jgbJHy4catNxVudhJcgR6NmVHfLApCjcPykKALD+oXHYklaKByf3MXvsmChvVDQo0M/fciN1a/S/X+Iiera3jL5pNmaAuMovaGvQK4K/uyPumxgluG/mgAB8sjMLAe62ZR6N7+tj17X1v6aNv7qlEjHeum4wAGBbelcp8LgIL/xnbgx2Z1Tg8en9dNlUxj+qnWQStHSUIZRJhfqw2j5Pw8wT4THmtod7mwZ5w72dca6qWWB0F6lEZDDHq4YE4/FfTHsh1Tu6YnvfeGzvGw8A8Gypx9i8VIzPO44JuckIaqi0eB3XthbMzjyI2ZkHAQApgX2xM2oUdkbFIc0/0qZsvnaV2uT5f7wzS3BsZ1Aot7IJ+89W4KZRYYLjAGB1ciGuHR5idj8REZE97H5XOGnSJKs1aZcsWYIlS5YI7gsNDcWePXsE9+nz8vLCihUr7J0eEREREdEld/FDJ4aLekILcs1tKpOmuaeK6syeL63IsOlzQ6vp3cDdCZyI1SrEluci4dwJjC44ibiCNLi3WV4QFNIkc0RyUH8cDYnFkZBYpARFo9nBye7zXCiWghZ9jDJIOhuY6x8T7u1i/RpGn2jBsl1WIiw+rnJ8f/coODtIDAIXg0I8MCjEco+DlffEQ6M5/yyUi5mpZYtHpvZFcn4NbhjBBdjuGBjsgd1PTbK55NkPd4+y6/xScdfCvKWMAv09ErEI94yPxD3jIw3GGH/p6pcBC/I0/XmiseOn+/nEbYV+fgR7OiG/utliAEculRg8tvV7s9bJHRtjxmNjzHhAo0FUVSEm5CVjfO5xjC44Ced24YyOTkNLzmJoyVk8sX8lyly9sCtyJHZGxWF/xFCzP5eb22zvU1VU24KC6mZMfm83AKBRYf7YJ35NZfCEiIh6DG+pISIiIiLqaRptKaKD2VWICXSH13k2nLbpkh0Lau0qtdka+q9uMMwyeXuz+Z4VDUalU/Z0sy6/uKMMV2dmyahuBksqnD1xJCQWR0MG4EhILNL9I6ESS6wfqMfH1QGVjW3WB56Hf83UlhkWWvz89b4EZJTWY2qMn8H2AA/tHfr6i8JygR4NAPDLktFY+PUhAKYLo0LLpBKJ9cXTif2617dCJBL1SGLPpcjUssTLxQHrHhp3qadxWYvwsRz8GxrqiZSCWoR7O9tdUkncjRZF5mIIcpnhz5AX5sXi6T9O4J5xveHuKMP2JybCQSLGhHd3AQDald3seSLYMt62Yzs5O0ghk4gNMguNCfV2sZtIhGyfUGT7hGLZyKvgoGzHiKJ0TMg9jvF5xzGwLNvi4f6N1bjpxFbcdGIrFBIpDoUNxpZ+CdjWZzQqXLvKezW1mQbkLRn/zi7dx/b2iUnOr0FClDeCBQJiREREljB4QkRERERkozal2qbFKbVGg7UpxXjslxT4uDrg6H+mX/C5dS7Lvb81E1/uEV7cOlFomGmy76zl0iz6bO7hodEguvIcxuWlYHT+SYwqOAUPhWnJL2uyvYJxNDhWl1mS1yvovEtwPTkjGs+uPmmwbXiYJ5Lza7t9zt/uT4CHkwwzPtwLAPBw0jZRlgh8mYwM74VRvbuyO5beMRJnyxsR37FNf1HY3NdZfKQ37hobgT+PF+Gecb0N9nUn8+Tv4O8WPKEL76tFI7DsQB5ujTdffskcmd43iqXSYPpf+uYCNMZByhvjQjEx2hd+HVkzffwMs8T0v3+FxOvtNwjY2PBtOCDIHWnF2ow/H1fTrB0XuQQOVoInoyO97MqOAbTPMau80ez+NqkMieFDkBg+BG/jTvg01WBSzjFMyUrC+LzjFsssylVKTMxNxsTcZLy25XMcC47Bln6jsaXfGMHeJrZKzKmyOka/YspPh/Px0+F85L011+bf40RERACDJ0RERERENnnjr9P4em8ONj82Hv0DDBtaH8yuxPb0ct1jDYCt6aUAcMEyHZoUSoOyJ50LReYCJwAsLpCdj4D6Sow7l4KxeSkYdy4Fvk21dp8jyysEh8IG4VDYIBwOHWRwh3JPeHRqX/QWuBs+0NMJOI/giXGPjs7lOqE7x40zRabG+Bs09NaPIVha3Htp/gD8Z26sSXaLSGCFtjt36V9sAn2j6Qrn7+6IZ2b379axYrEIR/8zDSq1Bk4O9mWfGdP/PnNzlOrmZmzHkxOxdH8u7hlvGLD0d5ejrF5b0mpiP198ffuIrnnaELi8PSEcS/fnYs6gADw8pS8e/yUFT86IhpeLA364exQqGhR48jdtzxJnBymkVjLJFgwJ0s3HVhP7+Vr93TClvx92ntH+jqt06YXfB03D74OmQaZqR1xBGqZmH8GU7CT0rikxew4xNIgrSkdcUTr+s+s7FG3qi0ljpiPJKQZnfCN6vD+V0M+VlIJaXP3ZATw2rS+GhHriaF41npgebbU3FBER/XMxeEJEREREZIOv9+YA0GZ2fHP7SIN9t3xz2ODxsXM153WtwzlVCPd20ZVzEjLsv9tM7kBuV12c5hGuimaMzj+JsedSMD73OPpUF9p9jmyvYG2wJFQbMKlwvXCNwr+/exQm9vPFkbxqk33mMjNemBeL/xqVOeu07M44fLEnGw9PEWim3hEB6c5inFJvtc9c2a5Otp5fehlETy5GWTu6sghlZnSHfo+Qvf+abHZclK8r3rhmkMn21Q+Mxdi3dgIAIn1dDM5nkPli5rzh3i5If3UmnGQSiEQibH5sgm7fhH6+KKnryupwlUsgM0ppk4hFUHX83Aj2dIJIJEKAhyM2PzYebo4ys89Hn5+bHEEejiiuaxXc7yqXosTMvnaJDAcjhuJgxFD8d+q96F1dhCkdgZRRBWmQqc33JgnOP4vg/LOYAuCcZwC29E3A5ugxSA7qf96BlJK6FuRWmmY8vrI+DQDwv+1nddv6+rnh6mHB53U9IiK6cjF4QkRERERkhwt5f+ofxwpR39qOV9anQywCct6ca3asceBEowF+Tsq/IPOSqpQYWpKBcXkpGJeXgqHFGZBq7AvU5PQK6sgsGYxDoQNR7uZ9QeYqpLOnx4iwXpg3OBAbTnTdHS2U9BDp64I7EsIxJMQD723NQGldK/Kquvq0TO7vh8n9/QSO7GLLXefGVHrBEwehul9WXK5lu169agCa25S4IyHiUk+FriC2fOnrByl7dSOIp99Dw7j6XKiXs01zcXYwvyzTy7lrTv7ujhgc7IEdHRkg902MxI0jQzH1/T0mx+lnR7o5StHQKlwiK8DdEbcnRMDZQYIX1qYJjpFKRDhdUm/+CejJ9QrGUq9gLI27Gm6KJkzMOYaZmYmYlHPUYnmv8NpSLDmyBkuOrEGhuy829h+PDf3H42RAn24FUhLe3Cm4XSWQjlJYY9iD6+V1aThVVIefl4w2CVbZo0mhxCvr0zB3cFC3+0oREdGlx+AJEREREZEdurMoDgCVjQokZldh5oAAg1IxGo0GIpEIB7IqdeVZAG3JkZfXpeGe8b0R0stZ6JQGqpra8KKZxa/uCK8pxsScY5iQm4zRBafgamHhS0ihux/2RwxFYkcZrlJ3nx6bW3eJxSJ8estwbDixUbdNqN/G9Fh/SCVijIzwwqolCfi/Fcd0wZN4Kz0POhmf1lJvhk4+rl0LpfY20QaAByf3waZTpYiL6IUjedrsJ1saxl9qgR5OWHnP6Es9DfoHGhHeC44yMSJ9XK0PtsL4Z8ndY3ujpLYV02L9kZRbhc92WW60LsRRJsEzs/tj5+ly3DAiFFcNDcYH2zJwa3w4BgZ7GIzVmOkd9N2dcbjhy0ST7XlvdQXnbxsdbjZ4Yvw774Mbh+BQThV+PWo547BB7oINMROwIWYCHJTtGHMuBTMzEzE96zB8muvMHhdSX4H7klbjvqTVOOcZgA39x2Nj//FI9+t93hkpQsET403LD+YBAPadrcCU/tqyim1KNd7floGJ/XwxJsq232Wf7srCr0cL8evRQoPXmoiILi8MnhARERER2cF47cbcgpWxaz4/gILqFjwypQ+emBENAHh+zUnsz6rExkfGI6O0weSY5QfzsO9sBXY8Ocnq+Ssb7atzb8yxvRWj809iUs4xTMw9ZrF2vZA6uQsOhg/B/oih2B8xFOc8A80udMUEutt8J/OFprah4Ub/AHdsOqXtYfPzvbYt8rerDTNzbCmzFe7tgg8XDoGXS/dKEg0M9kD6qzNRWteKKR13o18OmSdEF8KwUG3fJA8n8+WrXORSpLw4A9Ie6HlhHDxxlEnw36sHAgDGRnnjh8RzZjNALLl/YhTunxile/zmtYPtOn6QUZBFiKVgrfGe0ZHe8HaVWw2e6GuTyrA7Kg67o+LwvFqFEUWnMSszETMzExFSX272uPDaUjx46Dc8eOg3ZHsFY0NHRspZ33Cbr61PKHjywbZMODtIcM/4SIPtSlXX2BWHzuGrPTn4ak+OzYGQopquGw7WpRZj44livH/jULjKuQxHRHQ54U9tIiIiIiI7bDpVirzKJkR0NB+3MXaCguoW3fGdwZOVh7VltjakFps9LrvCsG57aV0rtqSV2jttUxoNIquLMCnnGCblHEV8wSnIVe02H94mluJYSAz2RQzDgfAhOBnQB2qxbc2bI31dLkjw5NCzUzH6zR12HSOUeeIoNXwe902MRLtKjakxfiZN3411ns3TaMHWWqPnTtcMC7FpnDnGJYAug5YnRBdELxcHHH9hutWm8o6y82s638lSHFYqESO+txe2nzYfKLhQzrcZunFgpU2phqu8+6+ZWizBkdCBOBI6EP+dcg8GlOdgRmYi5p7Zb7F/VlR1ER49uAqPHlyFDJ8wrI2dhLWxk1DkYbmEor6KBuGbDF7beNokeKIvv7rZ7D5z9F+2R34+DgCI3puDJ6b3s/tcRER06TB4QkRERERkRYHRwsni74/oskGEFt8tERotFotsrkay8OtEnKuyfyEHAJzbWpCQf6IjYHIMoXVldh1/2jdCGyyJGIqkkAFocbBeikrIwCAPbDxhW2ZLbx8Xwca/QvTLoXk4yVDX0m71ddVf8PzP3BisTy3G3eN6G4xxlEnw1Mxom+YwMlxb1svbVY7ld8XhzmVHAFzcDBD9xc7ulpkjuhJ0p49Jd9mahXixne/PHuPDw72d0dJuvhG8vSdP849Cmn8UPhx3K/pX5GHemX2Yd3ofImrN/46IrszH03t/wNN7f8Dh0IFYPWAyNkWPRb2j5fJrVU1t3ZpmT/0crenm9YmI6NJh8ISIiIiIyILfjxXiKb1eJIBhNojK3uCJwPjqpjYkZldZPbauud2+wIlGg6jqQkzOPoJJOccQV5gGucr2sjEVzp7YGzkcezsCJpUuvUzGjOvjg/1ZlbbPCcDicb2x5nghMssarY69eVQobokPR1pRHbIrmvDcmpOC4/r5u8LdsevPm9/uT8AHWzPx4OQ+Zs/9wKQogzncMz7S4t3HliQ9NxWl9a2IDepq1DwpuuuO6PO9+9se4V7OiO/tBXcn2Xk1PCYi21nrm+LpfPECOfqsZctZY3y0SCQ6r2wdH1e5cJlJkQhn/HrjjF9vvDd+EQaWZesCKZZKe8UXnEJ8wSm8uu1L7IiKw5qBU7A7cgTaJebLtdnL+MeoRqNBYnYVYgLdzQbohAIuF/P3ABER9QwGT4iIiIiILPhwW6bF/fbebNw5Xr9s1Vubzlg8RqXWIOq5v2w6v1SlRFxhGqZlJWFKdpJdvUuUIjGSg/tjT+8R2B05Aun+kdCILC++O8okSH91JmJf3GJx3NzBgdiWXoZ/z+oPB6kYj03rhwdWJludk0oNuMqliI/0Rnykt2Dw5MvbhiO+tzekEjFOvTITGo0Gbo4yfLlohOA51z00FlvSSvHQ5L749x8nrM7BFn7ujvATaArv6yZHRYMCU2P8e+Q6thCLRfjlvoSLdj2if7Lf70/AnswK3DEmwuK4Z2b3R0ldC24eFXZxJtZDxCIRgj2dUFTbgnBvZwAwCFSbkxDpjcQc05sCNj06HnGvb7d8sEiEUwF9cCqgD96aeCeGlmRi3um9mHtmPwIbhW80kKvaMSfzIOZkHkSNoxs2xIzHmtjJSA7ub1OjeY1GY/b3uXEAas3xIjzxayoCPRyR+OxU4acgdB5mAhIRXXYYPCEiIiKif7SDWZV4b2sG3rh2EPoHaLMGqpvaIJWI4O4og9Ko8XcnjUYDkUjUrbJdh3KqcNPXh2w+xlrgxLOlHpNyjmFaVhIm5ByDe5vt2Smlrl66YMmBiKFWy54Yk4hN+2wImRHrj49vGqa783ZajD9GR3oh+Vwt2lTCrzEAJER5GzwO8nBEcV2r7nGEtzNmDQzUPbalGe/gEE8MDvEEADw7pz+yKxpxe0L3GhBbs/6hcdibWYEFQ4MuyPmJ6NIaGeGFkRFeVsf5uMqx8p7RPX79MVHeOJhdhVtHX5ifYWIR8MPiUfhmbw7+b5K2cb23qxzPz4mBSKTtFyJkSn8/zB8SZBLw9nWT2zcBkQgpQdFICYrG61MWY2RhOq5O3415p/fBQyFc0rFXawMWHf8Li47/hdxegfht0HT8MXAKytx8zF5GqTYMnvx2rBAzBgQAMC191tl3rETvd5EtmHhCRHT5YfCEiIiIiP7Rbvn2MABgyQ/HsPfpyWhSKDH8v9sAAHlvzYVSJRwcaW5TwUUutdgkWEhuZZNdgRNBGg2iqgoxLfswpmYlYUTRGUg05gMQ+trFEhwNidUFTM74Rth0V645nXfSRvm6mDS31ycSiQxKljhIxVi1JAHf7ssRXHx745pBiA1yx9BQT4Ptv9yXgPHv7NI93v7ExG7PHQACPZyw8ZHx53UOSwI8HHFjXOgFOz8R/bN9e8dInCisQ5wNAZyrhgZhbUoxXr1qgM3nF4lEiPJ1xVvXDTbYfu8EbYnDLWmlOJJXY3Jcu1qNW+LDUNPchne3ZAAA3r5ukM3XFaIRiXXN5l+Zeh8m5xzBNWm7MCXrCBzUwiUpe9eU4Om9P+DJfSuwp/dw/Dp4Onb0GWVS1qtdpYZIL19kW3oZ7l5+BLcnhJtkjJgrv1Vc24IX157C3WN7C6aedLeEWnZFI9qUasQEugvuV6s1aGxTwt2x50qVERGRFoMnRERERPSP8ezqk8irbMKKe+JNFj+qOxq55us1h1epNVCaiY60tncGT6xHTyKe2Xges9aSqdoRV6AtxzU1OwnhtaU2H1vq6oWdUXHYEzkCB8KHolHubNNxk6N9sSujwuKYzsWgTY9OwM4z5bh/xTHBceaWjPSbmx/9zzSMfE1bzsXLxcEkcAIAoV6Gc5eypwcR/YM5O0gxOtLb+kAAY/v44KObhvXo9T+9ZTji39ihe3xTXCi2ppfhpjhtebLF43qjuU2JaTH+GBZm2jeru9qkMmzpNwZb+o2BR0sD5mbsx9VpuzCqMF1wvESjxpSco5iScxRVTu5YM2Ayfhk8A2d9tRk7GaUN8HYxzIrZeaYcO8+U45GpfQ226wdTzpTWIyW/FgvjQvH07yewP6sS20+X47rhISZz6M59ChqNBlPf3wMASH1pBjycTAMkty09jIPZVdj91CRE+LjYfxEiIjKLwRMiIiIi+sf4OSkfAHDsXA1G9Ta8S1csAprblNh4oqtHSJtSDZWZ4IlCqUZRbQvu/C7pgs3Xua0Fk3KOYWZmIiZnH7GrHFdqQF/sjIrD9j6jkOYf1a1VG1saHHeWM3GQiuHnbr4ci7la7/pbvfUa7xbW2P5ciYjIOuPyU7YQW4lP+xv1enrrusF4/RqN7gYFR5kE/5rZ3+7r2qPOyQ0/DZ2Nn4bORkhtKa5O341r0nYhqrpIcLx3Sz3uOboW9xxdi5TAfvh18HTc/mETGuTCgQep3s0W+VXNaFJ0ZbnM+t8+ANrfcfq/t4ReaolIBLVag4d+TkaYlwuemW39ddF/D1LRoBAMnhzM1vaB+f1YIZ6aGW31nEREZDsGT4iIiIjoH0cp0GNDLBbhudUn8WdKsW6bQqlCu5l+HK3tKkzpuBu0J3k112Ha2cOYeTYR4/JSIFe123Rci1SO/RFDsSMqDjuj4lDuZtudyJYMDvHAmuPCi0+d9BN4pBZKkphbs9PfLhKJMCTEA6mFdZhmocH6tcODsTq5CFP7+1mcGxERdelO5oPIbN6geebKWnWHWASD8pg+rnJUNirMji/0DMCnY27CpwkLMbz4DG44sQ3zz+yDa1uL4PihJZkYWpKJF3Z8i/Ux47Fi2BycCOhr8GLpP58J7+4SOg3WnyiG/q0W5hrGpxTW4q+T2sxRm4IndvZVIyKinsXgCRERERH9I7Qpu4IgQksRtc3tBoETQJtdYr5sl209RmwRUleGmZmJmHH2EEYWptvcv6TYzQc7o+Kwo88oHAwbDIXMzka8RgYEuSOtuB4AMK6PD26KC8Mr64VLoHTSr+FuLrtEu094u/Hm3+4fg9qWNvi5OQqOB4DXrx6E6TH+GN/P1+LciIioKwBhS18UoWNtNTzM0+7zW+Mok6C5TaV7/MPdozDn433WDxSJkBwcg+TgGPx36r2Yk3EAN57Yarasl5NSgRtPbseNJ7fjpH8UVg6djXWxE9Hs4ASNDQGMmuY2gzKeQr8OxWIRFHrvHball2F6rPkbBQBA3XNvNYiIqBsYPCEiIiKiK97yA7l4dUPXgomtN3Iq2s2X7Vp/olhwu000GvSvyNMFTAaU59h8aEpgX+yIGoUdfeKR7tf7vJq9G/vopmGY9oE2m+bJGf0glVg/t34ZGMvjbZung1RsMXACAE4OEsweFGjT+YiI/umOvzgDdc3tJj2jbGHLMZ/dMhyf7DyLd64fYtM53R2lqG81bfA+NNQTJ4vqDH7vOhkFT2KDTJum3xQXin1nK1FUK5xd0uzghN8HTcPvg6ahd3URbji5Dded2gn/xmrB8YPKsvHWlk/x3K7vsGbgZPxUMRvwjbD4nFRqw/cWVY1tJmOMA1H3/nAUeW/NtXxeZp4QEV1SDJ4QERER0RXvZaPsCY1g7okphVJldt8Xu7PtmoNIo8bwojOYmZmImWcTbW743i6WIDFsMLb0S8C2PvE9Uo5Ln4eTDDGBbnjjmkFwlEl02yViEaRiEUQiy8Em/XImjlKJ2XFmM096MPhDRESmPJxkgr0yzDn83FTkVjZh2YFcvLxggNXxcwcHYu5g2wPav96fgLkf7ze5OeGP/xsDhVKF2Be36LZN7OeL1VbKR7513WA0KpQY+NIWi+MAINcrGO9MvBPvj1+EiTnHcOPJbZialQSZ2vT3vXtbM+5I3og7kjfiSHAsVg6bjU3RY6GQmvYDO11Sb/B4x5lykzFikUjw/YdGo0FiThViAtzRS6/31w+JeXh942mrz0l3Hhvf2xARke0YPCEiIiKifxwzySQm1qeeR3YJtAGTkYXpmJNxALMzDiDAzF2uxppkjtgdOQJb+iVgd+RI1Du6Whx/9dAgRPq64oNtmXbPcd+/J8PdUbuoVtHQVUdeLBJBJBLh5MszoVJp0NyuRMKbO02O1y/b5eZo/s8Lc0ESxk6IiP4+HKRi+Ls7wt/dEaMjezZY36l/gDtOvjwDV316AGfLG3XbJWIRnB26fo88MCkKg0M8dcGTf3U0Q5eIRSaBF1e5fctbKrEEO/uMws4+o+DbWIMbT2zFzambEVJfITg+rigdcUXpeHHHN/h10DT8OHweijzs67ul1mgE64auP1GCR34+Dj83OZKen6bb/uLaNINxKw+fw+PT++l+ZxtjkgoRUc9j8ISIiIiIrhhqtQZFtS0I6eVkMaOhs365tTrmH+/MsnsOYrUKcYXpmJOxH7MyE82WBTFW5eSO7X3isbXfaCRFDUeDyPa7hEO9nPHwlD5oaVehoLoZG06U2Hyss162iUyg7FbngpQHhOejX7bLzcyCDmC+aJens+kdvEREdHGFeTkjv7oZEy9SLylnBym2PTERG04U46Gfjhvse/f6wcipbMK/ZkZj++muDI7OvlpiEWA+L9R+Fa698NmYhfhi9PWYmJuMW4//hSnZRyEWiHR4tdTj/qTVuPfIn9jadzSWj5iPw6EDbboT4H/bz+KNawaZbN98Svs7u1zvBgYhyw7kobxBgc9uGW7jMyMiovPF4AkRERERXTHe2ZKBL/dk4/VrBuLW+HCz4zpjJkfP1fTIdcVqFUYVpmHOmQOYlXkQfk22nbfQ3Q9b+47Gln4JOBoSC5VYG8iIi+iFI3m2z02j0WZ2/HtWf+w7W2FX8EQqEes+lul9bK7XizH9clwOUrH5cWZ2zRkYgD3DQzAivJdN1yMiop63aslo/JlShFtGhV3U64oEQus3jAzV299FqdJ2T9feHNHzaRZqsQS7ouKwKyoOwXXluCl1C246sQW+TbUmYyUaNWZnHsTszINI9+uNZSPmY13MRChkcovXeG7NSYPHdS3tdmWMbE0zX/KTiSdERD2PwRMiIiIi+ltTqzX4/VghhoZ5op+/m8WxX+7R9iF5Y+Npi8ETZUdgICW/ttvzkqhVGFVwCnPP7MfMzET4Ntt2rkzvMGyKHoPjIyZht1Ow4N2q0QFu9gVP9JZMxEbns9SzxEFiGNHQb/gu1KT29KuzMPm93fD3cERqQa32euaamRjxcBLOMJFKxHj/RtuaDBMR0YUR5OmEByb1uejXtRR0B4Ca5q7G6xWN2swMTyeZ1SyN81Xk4Yf3JyzCR2NvxvSzh3BryiaMO5cqODa2PBfvbvoYz+5ejp+GzsKKoXNQ6u5j03WGvLLV4PHKw+cwro8Pwr1dBMcLBZuIiOjCYfCEiIiIiP7WNp4swdN/nAAA5L0116ZjQr2cLe5v77h79fW/bG/ECmgzTEbnn8S8M/sx42wifJrrbDrujG84/ooeh43R45DtE4obR4bgbFYVUNtiMK6vnytWLRmNT3eZlgvr6+dqUBten6W7Vk+/Ogv9X9isezwo2AMni+qwasloRBsFo2R66SFqgcwTJwcJDj4zBQAw+JWtaFQoMbW/v8GYj28ehtSCWizdn6vb9sCkKAwP8zQ/SSIi+keaFO2L0ZFeGBziKbh/emzX75iWNm2xrqV3xGH+p/svxvSglEixqf84bOo/DpFVhVh0fCNuOLkdrm0tJmO9WurxUOKvuP/Q79gUPRbLRi5AcnCMXdd7fs0pOEjEyHx9tuD+NpUaB7MrMSbKtuAMERGdHwZPiIiIiOhv7Uxpvcm2U0V12J9VicXjehuUmuokl0nw+e4sTOjri4HBHib7H1iZjGdm97dtAhoNhhefwfzTezHvzD7B8h1CTvtGYGP/cdgUPRYF/uFoU6p1+6QSsWC/lW1PTARgmhECAD8ujsfoN3cIT1HvY+NyW8avz8p74yERieAi0FxXP4vEXNmuzjF7/jUJeVVNGBHuZbB/wZAgLBgSpAue+LjK8fQsG19rIiL6R5FJxFi1JMHsfv2+WE1tSgDAoBAPTO3vhx1nys0dZpNFo8Px46FzgvvWPTQWn+zMwrb0Mt22HO8QvDLtPrw/fhFuOLkNdxzbgIha0zKZUo0a88/sw/wz+3A0OAbfjLoG2/rEQy2WmIwV0qZSW9z//JpT2PXUJJvORURE54fBEyIiIiL6W3N2MH3LOu8T7R2nRTUtaFIo8X+TolDT3K7bn1pQi9SCWryzOcNstspbm86Yv6hGg5iKXCxI34v5p/cipN62BZo0v0hdwCTXK1i33VUiNgieOEiE2tB2EQoIGTdzd5VL0ahQmowzLrdlXFVLKhYJvqbGhIIr+rxd5fB2tVzbnYiIqKc0KbraxDs5WA5E2NI77P5JUbh1dBhm/W+fwfbn5vTH4BBPvHPdYAxL32ZyXKPcGctGXoXlI+ZjUs4x3HV0HSbkHTcZBwAji05j5JrTyOkVhKVxV+P3gVOt9kWxJreySXC7RgMs3Z+LZoUSD0/te17XICIiLQZPiIiIiK4gGo2mo5Hq5aczE8N4/q56i/jGz6/zjtGdGeWo1Que6Hv6d+Ea5UIiqouw4LQ2YNK3qsCmY076R+Gv/uPwV/RYnOsVJDjGQSoG9MqzyyQi3DY6HO9uyRAcbxw8uXpokMnrkvLidPR5fhMAw7JdxuW2jI8z7oli7K1rB6GwpkUwY6c7wryceuQ8RET0zxTt74aMsgbMHRSo2/bcnBhkVzThjgTh/mbPz43Fo6uO41xVs+D+DxcOQbCnEwAn7H5qEl5al4Y9mRUAAGlHCUtHmeUAjUYk1jWY71OZjzuSN+C6Uzvg3G7ajyWyphivb/0cT+xbgR+Gz8OPw+ei2rlnfs92UqnV+O+GdADA9SNDEOjB379EROeLwRMiIiKiK8SDPyUjv6oZax4YA6lA5sLfmUajwa3fHoZIBKxYHG+w4K+fAdHarha829Rc4AQAfj1aaPHagfUVmHtmHxac3ovBpaa9RoSc8o/Chv7j8Vf0WOT3CrQ63rgMVy8XBywZH2kQPBkS6qn7WCY1DHC0qzVwNnre+p9j/Ybx5sptdbIWPLlpVJjF/bb6/f4EfL03By/Mi+2R8xER0T/Tb/+XgLSiesT37ioTGeTphE2Pjjd7zOBgD2x7fCKWHcjFt/tzUWHUYH7e4K6bHSJ8XPCvmdFdwZOOTE+5lWb2+rJ8wvDCjAfw7oTbceOJrbjr6HoEN1SYjPNuqcfjB37C/x3+Hb8NmoalI69Cnl6mqj3qW9vh7ijTPU4t6OrD1tCqRGDPxmaIiP6RGDwhIiIiukJsPKGtu52cX4tRvb2sjP57qW5qw8HsKgDAb8cKEeLphDF9tM1Q9RcvyupbEeHjct7X82quw5yMA5ifvgfxhWk2HZPtFYJ1MROwPmYCcrxD7Lqeg95zcJVLceeYCJMA1w93jdJ9rN+4HQDalGrLd8DqZ57opaFE+Zq+VhLjOl4XyMgIL4yMuLy+DomI6O/H3VGGhChvu44Ri0VwEItw38QoTO7vh2s/P4irhgZh5eF8AKYZno6yrsedmSdiG35fOjtIEO7tgtMl2v5s9Y6u+HbUtVg+YgHmZOzHfYdXY0B5jslxjso2LDr+F249vglb+iXg89E34GRgV6ktob5o+t7ZfAaf787GsrvidNuS8qp1H1/3xUGcfHkmjufX4KnfUvHCvFhMivaz+nyIiMgQgydEREREVxhrf3BfbIU1zQj2dLJYTkx/Qf/p308AAE6/OgtODhKDYMDZ8kYorWRWmCNvV2DG2UO4On03JuYcg1RjuSErABS6+2JDzASsi5mIdL/emBbrj2tDPfHe1ky7rq0fPPlx8SiTniNOMgk8nLvuHq1rMcykae9oHnv/xCh8uScb02L8DfYbNozv+vjHxfEmc7lIsRMiIqK/hX7+bkh5cTqkEjEmR/vB3UlmMkYu7bpBQarXY6x/gBvOlDYInjfUywm7npyEJoUKQ17darBPKZFiXewkrIuZiDHnUrEkaQ0m5R4zOYcYGszOPIjZmQexN2IYPh2zEEmhA1HfYtrTTN/nu7MBAK91lOky1tCqPf7275LQ0KrEncuOmO0BR0RE5jF4QkRERHSF+TuFTlYcOof//HkKd42NwEvzB5gdJxQPyShrwNBQT4MyVJWNCjzys3BTViEijRqj80/hmrSdmJ1xAG5tLVaPqXD2xMb+47AuZiKOB0dDI+oKfNw2OhxVjW02X7+Tftku/bJZn986HC+tS8Nntww3GO/j6mDwWKnSvgZPzuiHCX19MCysl8H+MC9n3cf6DeODPE3rnV+uPXGIiIi6qzPbc1qsv+B+uV7miUwvePLLfQkY8spWoUOg0WjP6+5k4feqSISDEUNxMGIooivycG/SGixI3wMHtWlwZELecUzIO46kkFh815YFyKIAK7+zsyuEm8d36gyiEBFR9zB4QkREREQ9oqapDRtPlmD+4CBdFsUbf50GACw7kGcxeKJUm2aBVDVq65PrB0+a21RoaVdZnUvfinO4Nm0XrkrfjaCGSqvj6+Uu2NRvDNbHTEBi+GCoxMIlsqRiscEdqbaSSYWDJ3MGBWL2wACTgMaNcaEorVfgyz3aO0tHR2rLX8kkYl05MwD46d54HMyqwk1xobptw8M87Z4fERHR5e7OMRFYfjAP902MtPtY/dKY7cqu9x0eTjLcEh+GnzrKfenrvFdB/3f4g5Oj8NmubN3jPn6uuGdcbzyz+iQyfCPw1NzH8e6ERbjr2HrccnwT3NtMG9qPKkzHqA8fw3T/KHw2+gZsjh5jcCOHrZQq6xm2RERkGYMnRERERFcAdTdLWfWkB1YmIzGnCttPl2F5R/8O/QpipXWteGTVcdw5JgJzBhk2WReInUCl1qCuuR2vdwRgAKBJYf4OSt/GGixI341r03YJ1hc31iKVY3ufUVgXOxF7eo9Am9S0jIcxiVjUrZ4hcv3ME6P1D6FMEGcHKZ6Z3R+3xofhQFYlrhku3Ex2TJQPxkT5GGwL6eWM3U9Ngqez6fM5+MwUu+dORER0OXhhXixuGBmCmAB3u491k3ctj1U0GjaXf3XBANwaH4a5H+832K5fJnXzY+ORVlSPa4cHGwRPlCq1yfuGMjcfvDXpLnyasBC3pvyFe5L+hG9zrcmcBpZl44u1byHLKwSfJ9yAdTEToZTYvozXqmTwhIjofDF4QkRERHQF0O8LcqlaniTmaBu+786oENz/4tpTSMqtRlJutUndbZXApNUaDV7bmI7a5q7+H9tPlxmMcWprxYyzibg2bRfG5aVAYqWPiRoiHAgfgjUDJ2NL3wQ0yZ0tjjemUmsES4zpu2ZYMNYcLzLY5mAm88SaUC9n3DQqzK45AkCEj2Gj+H1PT0ZdS7tgGS8iIqIrgUQswoAgj24dKxKJ8OjUvvj1aAGuHmZ4w4JUIsaAIA8kPjsFpXWtuObzgwAMS472D3BHf4GgTbtKY9KcvlOj3BlfxV+P5cPnY+GJrbjv8GoEN5i+h+pTXYgPNn6Ix/f/hE8SFmL1wCk2BVFa2qxn6lpTVNuCl9elYfG43hgd6X3e5yMiutwweEJERER0BdD/A17zN+p6oj+X0vpW3cdZ5Y34ck82HprcBxE+LoKZM/evSDbZllXeCJFGjYRzJ3DdqR2YlZkIl/ZWk3HGTvtGYPWAKVgXOwFlboaZGtcOC8Zqo2BHgLsjXpofC1dHKRYtTdJtV6rVBneaChGKjegHTy5FcCvUyxmh1ocRERH9Yz0+vR8en97P7P5ADycEenTdhGDL+612gcwTYwqZHD+MmI+fh87C1Wm78ciRPxBaWWgyLrSuDO9s/hgPHvoVn3YEUcyVGQWAd7ecMXj8c1I+5gwM1JVWtcW/fkvFwewqbEsvY8N5IvpHYvCEiIiI6AqgvsAr8hqN5rwbjSvau7JCpn2wBwBwsrAOWx6fYNDXxJzQ2lJcf3I7rju1AyH1wtkt+kpdvfBn7CT8OWAyzvj1tmuuv96XgDBvZ4NAydVDgzC+ry/WphSZPW7xuN5oFGjOqt8wXqi/CxEREV1ezL11EYu69rWr1JDaWO6zXSLDb4On49C4uRhyeDseTPwVMRV5JuPCa0vx7qaP8GDir/h47E1YGztJMIjy61HDAMyzq08ip6IRz8+NtWk+AFBY02LzWCKiKxGDJ0RERERXgAsZO/kxMQ+f7srCisXx6Ovv1u3ztAk0Ls0sbwAgXLYLAJzbWjAn4wCuP7kdowtOWb1Gk8wRm6PHYPWAKUgMGwS1hTsyAWDu4EDB+0Y740QikQi7n5qEVqVKV47DeLHESSbRNbF/YV4sSuta8cvRAoMx+g3jlX+D/jRERER0fsy993KQitHaccOIl4uD3b3SlCIxNsRMwIb+4zEl+wgeSvwFw4szTMZF1Jbgg40f4qGDv+DjsTdjXcwEq+97vtmXaxA8OVFYC7lUguiA7r+/IyK6kjF4QkRERHQFMAg+nMfavFKlxprjRciqaMQzs/pDJBLhhbVpAIAX16bh5yWjbTrPU7+l4tGpfQ0WFnIrm0zGuXY0aDUo26XRYFRhGq4/uR1zz+y3WpZLJRJjX8QwrB44Gdv6jEaLg6NNcwSA+ydEYel+0+by+gsdxv1DjEuMLYwLxbg+PujXEVgK8HDEiZdnYPoHe1BWr206K9M7ny1ZNkRERPT39N+rBuCV9en4+KahgvsdJF3Bk89vHYGi2ma7zl9S1/G+RyTCzj6jsDMqDhNyk/H4/p8wrMQ0iBJZU4z/bXgfDx/8BR+NvQkb+o+3GETJr2pGmLczCqqbseDTAwCArxeNwIwBAXbNk4jon4DBEyIiIqIrgEHD+G6eI6u8EXM/3geFUvsH/5RoP8TrNQc1lx0CAN/sNQxA/H6sEKkFtVav6SaXIqu8Add+cRBB9eW49tROXH9yByJqS6wee9o3Ar8PmoZ1MRNR4drL6nghIpHw62WpqbtxiTSNRoNpsf4G29wdZTjw7yno8/ymjgt17VOqGDwhIiK6XC1KiMDNo8IgNdMIfmK0H9anFsPHVY7oADfkV9sXPDEhEmFv5Ajs7T0ck3KO4bEDKzG05KzJsKjqQny8/j08fPAXvDdhEbb0TRBsxFbf2g4AOJBVqdv2+C8pSHt1lslY/b4uB7MrMSbKx2SMJUqVGttPl2N4uCf83Gy/uYWI6O+CwRMiIiKiK4CmB9povL81Qxc4AYA1x4sMgifmanafLWvA63+dNt1e3mj1mlWVdfj4nlfx+YntGHsuFWIroZ8aRzesjZ2I3wZNQ5p/lHB3djt5OJk2ThULr4cAABxlhndzmpux/qKKCCI4SMRoU6kRG+jenWkSERHR34S5wAkAvHb1QPQPcMOCIUEAgOY2015o3SISYXfUSOyOHIHJOUfx+P6VGFyaZTKsb1UBvlrzBlIC++HtiXciMXywwf7mNhVWJxfimdUnddua2lSoaFDg16MFuG54CAI8TAMdmaUNdgdPfjx0Dq+sT0cvZxmOvzjDrmOJiP4OGDwhIiIiugJciIbxq44U4I1rBukeG9fs7ixfddvSw/adWKPBoNIs3HRiC+an74V7m+U7MlUiMfb0Ho7fBk3Djj7xaJOaBjvOx2PT+iGzrAGjIrzw8U7tIoSlzJM5gwKxNqUIuzK0TetnDwy06TopL01HS5sKHs49O38iIiL6+/BwkuHByX10jxsVPRQ86SQSYVdUHHZFjsTU7CQ8vv8nDCzLNhk2tCQTP696DnsjhuHdCbfjZGBfAEBacR1eWZ9uMj7u9e0AgLUpRdj6+ES7pqRUqQUDSjvPlAMAaprb7TofEdHfBYMnRERERFcA/ZJa3Y2jCB2n39xcP6CgVKkx/9MDcJCKdX09rHFvbcRV6btxU+pWDCg37TNiLMsrBL8NnobVA6agwtXLpmt0h5eLA1YtScC5qiabgicOUjGW3TUKTQolimpbdL1OrHF2kMLZgW+/iYiI/kmCPJ1Mtg0O8cDU/v7wcXPAaxtOo6VdZfEct8SH4afD+YYbRSLs6BMPzJ0H7x2bcee25YgtzzU5dkLecUzIO46N0WPx/vhFeGW95flmllnPHNb3+e4s/G/7Wfxx/xgMCvGw61gior87/vVGREREdAXQzzxRaTR4bs1JRPm6YvG43ud13nZVVxkvqViE1nYVfjtaADdHGU6X1Fs/gUaDuMI03JS6BXMzDsBR2WZxeL2DM9bHTsDvA6fheFB0j5TlAoD5Q4KwPrUYDlIx2vRKk8nMlN2Q2HBdF7nU5sBJDz0NIiIiusxM6ueLF+fFop+/G34+ko/J0X64fkSIbv+Evr4Y/84ui+fQWLgz5qrhIdjnehXmBg/DvNP78OS+FYK94+ZmHMDMzET8NmgaPhp7C0rdrZfgKqhusTrmnc3aJvYvrTuF1Q+MNdgn4hsgIrrMWajmLGzv3r2YP38+goKCIBKJ8Oeffxrsv/POOyESiQz+jR492mCMQqHAww8/DB8fH7i4uGDBggUoLCw0GFNTU4NFixbBw8MDHh4eWLRoEWpra+1+gkRERET/BPp/Ux/OqcJPh/Px3w2mJRmEVDYqMOejfdicVmqyT7+5uVgswuO/pOCFtWl47JcUi+f0aq7DvYdXY8e3/4fffnoG16XtMhs4UUOEvRHD8Mj8pxD30I94fuZDOB7cv0cjDp/cPAyZr83G/n9PNtjez99VcLzI7nfJRERERKZEIhHuHtcb4/r64LNbhhsETgDt+ytrVGrzwROZWASZVAyNSIz1sRMx7Z4v8NzMB1EqkLUr1ahx84mt2PP1vXh213dwbzWfZdIqkA2jVmt0ZVuNCQVKGDohosud3ZknTU1NGDJkCO666y5cd911gmNmzZqFZcuW6R47ODgY7H/sscewfv16rFq1Ct7e3njyyScxb948HDt2DBKJtgHnLbfcgsLCQmzevBkAsGTJEixatAjr11vJLyQiIiK6gmw4UYzSulbcMz7S4jj9zJOGVvtqa3+2KwvpZrJImtu7ziUVi7DplGmApZNIo8a4vBQsTN2KGWcPwUFteR6F7r74dfAM/D5oKord/eya851jIrD8YJ5dxzhIxfBzM2yAau6OSEtlu+zRy1mGmuZ2TIux7/kRERHRP4MNsRN4u8rN7pNKxHDQy6RVSqT4aehsrB4wGXckb8D/HfodnkZBErmqHfclrcaNJ7bho7E3Y+Ww2WiXGPZkyyhtMHisAbDgs/0AgHUPjjMJ+lQ2mpZxZeIJEV3u7A6ezJ49G7Nnz7Y4Ri6XIyAgQHBfXV0dli5dih9//BHTpk0DAKxYsQKhoaHYvn07Zs6cidOnT2Pz5s04dOgQ4uPjAQDffPMNEhISkJGRgejoaHunTURERHRZeuin4wCA8X19ER1gvkSU/k2AeVVNuo8PZldiaKinSa+NlYfP4eMdZ/HD3fFobVfDnPmfHNB9bO7OSP+GStxwcjsWntiG0Loyi8+nXSzBtj7xWDVkJvZHDIVaLLE43pxezl035yy/Kw47Tpfjx0PnunUuIbaU7bLFjicn4WxZA0b1vnA9W4iIiOjyZct7jgcmRSG3ogkLhgbhgZXJBvtkEhFkEtNztMoc8VX89fh5yCwsSVqNu4+uhXO7YYCjV2sDXt7xNe5IXo+3Jt6FLf0SAJEIE97ZZXLOopoWnCrS3mxT29IOLxfDG6XPVTUjp6IRkb5dWb2MnRDR5e6CFCTYvXs3/Pz80K9fP9x7770oLy/X7Tt27Bja29sxY8YM3bagoCAMHDgQBw8eBAAkJibCw8NDFzgBgNGjR8PDw0M3xphCoUB9fb3BPyIiIqIrRXWT5V4h7Xp9PPadrdR9fMs3h3Hfj8dMxj+/5hTK6hV46rdUmGn7AcDwLkL9P+7FahWmZh3Gt7+/goNf3I2n9q2wGDjJ9grGG5PuwugHvscD1zyHvZEjuh04AbR3Mj4ytS+mx/pjfF9feLs6WD+ow8c3D4NYBHx+63CL5+8JXi4OiI/0Zs1vIiIiEmTLewQ3Rxm+XDQCcwYFYsGQIIN9rnKp2R5uAFDv6Ir3JtyOiUu+xffD56Jd4P1X75oSfPXnG/j1p39jSHEG8qubkV3RZDDm2/1dzej1e+Lp25pu+F6wpzJ5iYgulR5vGD979mzccMMNCA8PR25uLl544QVMmTIFx44dg1wuR2lpKRwcHNCrVy+D4/z9/VFaqi0DUVpaCj8/09IGfn5+ujHG3nzzTbzyyis9/XSIiIiI/hY0MF/r+vuDeXhpXZrZ/fvOVqKyUQEfgZIPJ4vqEODhKHCUqXWpxfBtrMbCE1txc8oWBDdUWBzfKnXAX9FjsWrITCSFDDjviMTdY3vjuwPaP9ybFEo8OydGt++usb3xv+1nDcaPjvRCsKcz7hobYbB9wZAgzB4YYHGhgX/rExER0cWgn9j7xjWD8OOhczitV051cIiHwfjXrxkIF7kEPycVANAGViy9p+lU4doLL03/P3w38io8ved7zM04YDJmVGE61v74JNbFTMA7E+9AoYe/4LnalMLBE+O3T7x5hIgudz0ePFm4cKHu44EDB2LkyJEIDw/Hxo0bce2115o9TqPRGPxQFfoBazxG37PPPosnnnhC97i+vh6hoaHdeQpEREREfz96sRO1WoNXN6RjdXIhHprSB2/8dcbq4Y//koIfF8ejUaGEq9zwLeC2dMultqDRYMy5VNyasgkzzh6CTG3aQFTfad8I/DxkJv4cMBn1jsIN2btDLutaGGgzuuPRw0mGaH83ZJRp63NPj/XH29cNNikp0UlokcFTrxRYT5XtIiIiIrJEf51rWqwfrhkWjO8O5GJajD8qGxUmwRM3RxkWj4vUC55I4SDtel9z48gQ/Hq00Oz1zvUKwoNXP4ulhafxn13fYnhxhsmYBaf3YmbmQSwbsQCfjVmIBrmLwX6FUvi9oPHbJ76dIqLLXY8HT4wFBgYiPDwcZ89q7wQMCAhAW1sbampqDLJPysvLMWbMGN2YsjLTP+IrKirg7y8c9ZbL5ZDLzTfQIiIiIrrcqNXC2SaHc6t1zdJtCZwA2uyT7/bn4tUN6Xh5fqxNx3i0NOD6UztwS8omRFUXWRzb6OCEdTETsWrIDJwI6HtB/lrWP6NQuYgJ/XyQUdaAXs4yfHP7SLvP7+Ekw+/3J0AmEUNqwx2cREREROdLrel6vycRieDkIMGDk/sAAKIh3O9O/22Wu5MMUr30lUem9oWbowxL9cps3TcxEkEeTgaZyskhMbj2tvfwQEUyblr9OcKMyq/KVUrcn7Qa15/agXcm3IHfBk+DRqR9f9TarkZ+VTMmv7/b4nNj7ISILncXPHhSVVWFgoICBAYGAgBGjBgBmUyGbdu24cYbbwQAlJSU4NSpU3jnnXcAAAkJCairq0NSUhJGjRoFADh8+DDq6up0ARYiIiKiK9XPSfmQiEW4Zliwbpt+GKWqSWF6kA1e3ZAOAHh5fbr5QRoNhhVn4NaUTZh3Zh8clZZ7raQE9sVPQ2ZjQ8x4NDs4dWtettJfKBAqF/HkjGiEe7tgSn/T8q+2GhnBxu5ERER08ejFTmzuEaJfitXFQWISTPnP3Bhd8OTL24Zj1sBArE0RuBFGJEL57KswzWswbk9ej4cP/gIPhWGvE5/mOryz+WPclvIXXp56H5JDYtDarsK9PxyFyuhGH7FIBJVag+2nyzA60tukBwoR0eXG7uBJY2MjsrKydI9zc3ORkpICLy8veHl54eWXX8Z1112HwMBA5OXl4bnnnoOPjw+uueYaAICHhwcWL16MJ598Et7e3vDy8sJTTz2FQYMGYdq0aQCAmJgYzJo1C/feey+++uorAMCSJUswb948REdH98TzJiIiIvpbqm5qw7OrTwIAZg4I0G2/78dj+OP/xiA6wM3kD9We4NzWgqvTd+PW45swoDzH4tgWqRxrYydixbA5OBXQx+y4m+JCsepIQY/NUaR3/2K7yvQ1cJRJcNvo8B67HhEREdGF5uPqgNGRXpCIRfB0ltl0jIeTDJseHQ8HqRgikQiOsq4m8PKObZ063zaa64vy/JwY/H6sEN+Ouha/D5qGhw/+gkXJG+GgVhqMG1yahdUr/4U1sZOgmvsRSupaBc/3nz9P4eekfNw9trfV5/HVnmz8kHgOv96fgGBPyzfhZFc0QgQg0rfnSsISEVljd/Dk6NGjmDx5su5xZ5+RO+64A1988QVOnjyJH374AbW1tQgMDMTkyZPxyy+/wM2tK9Xwww8/hFQqxY033oiWlhZMnToVy5cvh0TS9cN+5cqVeOSRRzBjxgwAwIIFC/Dpp592+4kSERERXQ6a27r+UP3jWFe96kaFErd+exhH/zMNSoHAQXdFV+ThtuN/4eq0XXBra7E4NtM7DCuHzcYaG3uZaOycpq+bHBUN5rNqxFYyT4iIiIguNyKRCD/fO1r3sa1iAt11H7s5di3vORgFSTrLgknEpucWi4Beev3hap3c8d+p9+KH4XPx/K7vMOPsIZNjrknfDeXMBDwQdz2Wxl0NhbTreJFIhJ+T8gEA3x3INTm2U1Z5I4I8HfHmJm352Xc3n8H/bhpmMk6l1iCjtAGRvi6Y+v4eAEDGa7Mgl0pMxhIRXQh2B08mTZoEjYW/hLds2WL1HI6Ojvjkk0/wySefmB3j5eWFFStW2Ds9IiIiosua/tuszjJbnSobtYGF8808kaqUmJmZiDuS12NUoYUSXgDaxFJsih6LlcNmIylkgF29TNQ2Rk+2PzEBffy0N9q0q9To+/wm4YEibSmzNceLsGRCpM3zICIiIvo7sydoIsTf3dHsuTS6zBPTa3S+pVz30Fi8+dcZJOZUAdA2lV9y7X8wPjcZL+74Bn2rDDOJpS3NeHrvD1h4Yiten7wYW/uOBkQim3qcHM6pwsKvDyHKt6sJfbvAe9vyhla8vyUTvxwtwO0JXZnFTQoVgydEdNFc8J4nRERERGQ7oUboxpTdDJ74NtbgptTNuDVlEwIaqy2OLfDwx09DZ+HXQdNR5eLZrevpz9LdUYr6VqXJmGV3xukCJ4D5khKAtunoBzcOwcsLBsDDybayFkRERERXuoRIb9wUF4pw766AxI0jQ3D0XA2mx/oDACRi8++xBod4YumdIxH7ouEN0ft6D8fyz/9E8E/f4bbNy+Fu1A8lvLYUX695HXsjhuGl6fdDJIq1OM9GhRJ/phQDALIrus5lfJP26ZJ6zP5on+7xD4nnzI4lIrqQGDwhIiIiugSaFEoczK7C+1sz8ODkPpg/JAgA0GYleFLVqIBKbUfJqo4G8Hckr8ecMwdM6lfrU4nE2BkVh5VDZ2NP5HBoROb/yLaFfubJj4vjcdVnB0zGDA/rZfP5xCIRRCIRAydEREREekQiEd66brDBtneuHwKNRqPLRJEJlO3qH9B1A4uTTDib44EZMQi+8VMsemsWZq/6FDelboUYhgGMCXnHsfm7B/HVqesgT7gRCpnc5DwrD5/D82tOwUFq+v7S+K3tmuMCze07xzJ2QkQXEYMnRERERJfA1Z8dwNnyRgDAwz8f1wVPdp4pt3hcdkWTTZkncmUb5p3ehzuS12NwaZbFseUuvbBq8AysGjoTxe5+Nj4DG+hNc3CIh+AQCzdBmjjPihZERERE/yj6JbyMe54MCHLHF7eOEByrr/OmlWYPLzw362GsHDobL2//GnFFhqVf5SolHkn8BVen78ZL0+/Hrqg4g/3PrzkFQLhvnVqjwcc7zmJIqCcm9vO1+JyUHZGWxOwqJOZU4dGpfQX7uRAR9QQGT4iIiIgugc7AibF3NmdYPK5JobTY8ySovhy3Ht+Em1K3wLul3uK5jgTH4ofhc7E5egzaJZazOR6Z2hcf7zhrcYwx/cwTc3+QC/2x29nXZFwfH+zPquw6h11XJyIiIqJOYqP3XO/dMARh3s5Wj3Nx0GakdL5nSwvogxtufRsLTu/Fs7u+Q2BjlcH4sLoyLPv9FWzul4BXp95r0405W9PLsDW9DACQ99Zci2OVKu37y5u/0TazD3B3xC3xYVavQUTUHQyeEBEREV1GGoWCJxoNEvJP4o7k9Zh+9jAkGvNlvVqlDlgbMxE/jJiHNP8om69799gIfLknW/BuQQD479UD8cKfpwynZcN5xQJBldevGYjJ/f0wKdoX+VXNmPfJfgCAXHZ+ZcSIiIiISMvW1iGdN8BI9N+ziURYFzsR2/uMwiMHfsbio2shU6sMjpuVmYgJucn4aOzN+G7kVVZv1LGVcQZ2lpkbkoiIegL/AiUiIiK6wOpa2rH5VAla21Vmx6w8fM7sPn1NCqXuj0antlbcevwvbPnuQfy86jnMykw0GzgpdPfDm5PuxOgHluPfcx61K3ACAHKpBCPDzfcnCfJwNNl27/hIAMC8wYFmjxMKnjg7SLFgSBDcHWUYGOyBx6b1xYAgd9wSH27XnImIiIhIyzhYEijw3s0SqcT0PVuzgxPemnw35t75EZJCTJvFO7cr8Ozu5di47FHE55+06Tqf77Zcbta4959dvQCJiOzEzBMiIiKiC2zx8iM4eq4Gd42NwK3xYXh3i2lprufXnMKU/tbLGrSp1Ni+OQnP7P4DN6dugYeiyeL4feFD8f2I+dgZNRJqsXAjUABIiPRGYk6V2f0yiQhvXzcYL69Lww6BvixCQZCBwR5IfWkG3B21bzmX3RWHu5YdMRhjS43qx6b1w2PT+lkdR0RERETWrX1wLHq5OJhsf/PaQXhvSwbaVGo0tCoN9gm91+uU6RuBG295G9ed2olnd38Hn+Y6g/39qvLxy8/P4tdB0/D65MWoc3IzcybrJWzbVYZRoHZ2kCeiC4iZJ0REREQ9YF1qMU6XCPcYOXquBgDwx7FC3LnsCLaklQmO25BaYv4CGg2GF52G192347d3F+H+pNVmAyeNDk74fvhcTF38BRbd9Bq29423GDgBADdHKVYtGa17PCDIHc/O7q97LBGLEOrljKV3xqGXs2nZBXN/T3s4yXTlHiZH+2H/vydjUHBX83j29yQiIiK6uAaHeAhuv3lUGI7+ZxpiAt1N9lm94UUkwh+DpmLqPV9ixdDZUAt0q7vx5HZs//b/MD99j+11w4wojYInKhWDJ0R04TDzhIiIiMgGSpUaH+/Mglwqxt7MCry8YIDuD8v9ZyvxyM/HAVhvcllY02J23+t/nTbZJlUpMSfjAO4+uhZDSzItnjvbKwTfD5+L1QOnolFuvQGoPrUG6OffdRfgdcNDMD3WH29uOgPAsOF7uLcLapprDY63dDeivpBeznhhXixu/CrR5LxEREREdOFZev8lEomgFsjmsCVbGADqnNzwn5kP4rdB0/Da1s8xqCzbYL9vcy0+Wf8urk7fjRdm/J9NDeX1KY3KdBn3QCEi6kkMnhARERHZ4JejBfh4x1nd4/tXHMOef00GAJws6ipNMOr17ShvUOCZ2f1x/8Qog2wUe26w82ypx82pW3D7sQ0IbDRfTksNEXZGjcTyEQtwIGIINCLhxOLbE8LxQ6L5vioajcagEahMos002fDwODjKDLNWPlw4FP/dkA65VIxNp0oB2P4HNRERERFdfCG9nGweqxJ40yq1871ealA0rrr9A9x2/C/8a+8PcGszvIFoavYRxC89hffGL8IPw+dazJJ2cZCgqU3bO9A4WGIcTOn07OoTSC2ow5oHx0AutZyBTURkDoMnRERERDbIKm80eFzd1Kb7WL9RZXmDAgDw1qYzuG9CJE7pBVYaFIa1o4VEVRbg7mNrce2pXXBSKsyOa5I54tfB0/H98HnI8wq2el5PJ9NSW/rUGg0k+o1AOwIpA4NNyzr09nHBd3fGYen+XF3wxPgGxn/P6m9yXCdXOd+CEhEREV1MQZ5O+OmeeLhbeU8IQDDz5Inp/XTv+2ylFkvww4j52No3Af/d9gWmZx022O/a1oKXd3yNq9L34JnZDyPDN0LwPE4OUl3wpLFVieyKrvfl5jJPfk4qAADsyajAjAEBds2biKgT/3IlIiKiy96+sxX4fFc23rx2ECJ8XC7INYz/iNQPAJj7o62lXQWVLaUENBpMyE3G3UfXYVLuMYtDC939sHzEPPw6eAbqHV1N9ns4yVDX0m6yfUI/X3y8M8vsedUa7V19nYoslBfrpB8v0S/blfnabDhIzbfWiw1yxwOTohDo4Wj1GkRERETUM8b08bFtoEBZr77+brhrbASWHcjTbZs7KBDnqptwqki471+nUncfHP3fd1j9zY94ZftX8GuqMdg/rCQDG5Y/iq/ir8MnY26CQmrYzL5NqdJ9fNfyIwb7lCrTzJOy+lbdx5llDTheUIv7J0bBw4bAERGRPgZPiIiI6LJR3tCKNclFuH5ECLxd5brti5YmAQAe/SUFax8ce0GubVy+wEUvePK/7WeNhwMA6luUFuswO7a34tq0Xbjr6Dr0rSqweP0jwbH4buQCbO2XAJWFsgaBHo4GwZOs12ejpV0FmcR8MAMANNDWuB7V2wtJudWYNzjQ4ngAcJF3zUM/eGIpcNLpaQuZKURERER06bx5zSAsWnoYj03vZ7D92dkxuuDJkBAPvDQ/Fnd/f0TgDMDkaF/syqgAAPTxc4W7swM29R+HAxFD8czuZbgldYvBeJlahYcSf8WsjIP415zHcDy4671ifav57G3jBvIAMOGdXbqP39uq7RlYVt+KD24cav5JExEJYPCEiIiILht3Lz+CU0X12J1RgZ+XjDbZX9lgvszV+TK+qU0/S8Och39OxqRo0yaY3k21uD15IxYd3wivFvN36rWLJdjQfzyWjVyAE4H9zI7T56w3r7mDAyGViOHWETh5dGpffLRDONCj6QgO/XD3KFQ0KBDqZb3h/NXDgrHhRAnG9vFhFgkRERHRFSI2yB1H/zPNpLG8g1SMCf18kV5ch5/uHQ0XuRRjo3xwqqgebo5SNOgFOZbdNQoRz2wEoH2f2ZmNXe/oiudmPYy1sZPw5uZPEFlTbHCNPtWF+H3l0/gm7mp8OP42kywUYzvOlCO3sgm99bLPFUrTbJQThXUm24iIrGHwhIiIiC4bnSUBEnPMN1C3l1qtQWWjAn7ulhf/jct2pRbW4aavE/Ha1QPNHnMkrwapBV1/qEVWFeKeI3/iulM7IFeZltbqVOPohpXDZuPHYXNQ5ma9vML2JyZi2gd7ABhmxLwwN9ZgnH6pgoUjQ1FQ04xADyf8kVyIhyb3AQA4yiQ2BU4AQC6V4MfF8brHX942HJ7Olv/AJSIiIqK/P+PASafv74qDUq3RZTU/Nq0fQno5YXJ/P4x7e5fgMRqYlrk9HDYIs+/+FA8d/AX3H/4dMnVXaS6JRo37k1ZjWlaSSRaKkH//fgK/3p9gcYxGY72U7s4zZfh2Xy7euX4wQnrZ9n6YiK5sDJ4QERHRFcPM33gWPfZLCtalFmPZnXGY3N80S6STcdkuADiUU437VyRbPH+bUoW4wjQsSVpj0iTT2FnvUHw38iqsGTAJrTLbMjluGx0GqbjrietnngQYZYOo9Z7D29cPBqD9Q/KFeTE9EvSYNdB6qS8iIiIiunyJRCLIJF3vPZ0cJFiUEGH1OJXaNBtEIXXA+xMWYUPMeLzz10cYUmqYIW1rFsqp4jpoNBp8vCMLPx46Z/NzaW1XwUEihrjjvfTdy48CAJ5bcwo/3D3K5vMQ0ZWLwRMiIiL6R1uXqi0V8MXubIvBE+PMk05Z5Y2C28VqFWZmJmJJ0hoMK8mwOIc9vYdj6cirsLf3cLsiQHv+NQmhvZxxrrpZt83FwfzbO/0gSyeRSMRsESIiIiK6cDTAotER+GxXtuDuDN8IXLvoPdx3+A88euAnyFVd5b9syUJpblPhnu+PYseZcpunVNPUhmH/3YYR4b3wx/+NMdhX1XjhSgET0eXFejdPIiIiostEZ9whvbge7245g0aF+eaSxsRW3hW1W2j8rs+prRW3H1uP3V8vwRdr3zIbOGkTS/HbwGmYcfenuOPGV7E3coTdqTPh3i4Qi0UGd/LNHBgAAHAQaBB/w8hQDAhyx8NT+th1HSIiIiKi7tJAmxH9xa3DddtGR3oZjFGJJfg84UbMv+N/SA3oa3KOziyUZ3Z9B7myzWS/tcCJ8Tv5nR3jj52rMRnbnWx2IroyMfOEiIiI/p+9u46O4mrDAP6sxt0DwZ3g7u7u7q6FIi0FCpQWbZGvUEpxh+JW3DVocIegCUmI2/r3R8okk92N0EAgPL9zON/Me+/cvXPOV9jZd+59sw0JEp90mv7vDAAgOkGLn1qZr0mSnDTFU5Lf03f4ZrM/WpX2xvC6BfA2MiHV691iwtHz2j70uL4fjgmmV6MAQJSFDdaXaYLVZVsg2M5FiMulEqO9oJN7/EsTFJh4QDhvWzaHcJz8ugZFPbBpQGXkd7dBSjYWcuwfWSPV+yAiIiIiykzv640o5Ukv98xqWxK1fz1p1PdhOlehjGoxFrc9M/BCUIqv2am9OJXyuYCIvl5MnhAREVG2kfI559qLcDwOjkEBd9s0r5Wl2NKqz+rLiFPrsPT0Uyw9/dTsdflDX2LA5Z1oc+e46OEupVf27lhRoRX+LtEAsRbGBSgVMilW9C6HfqsvY1qr4giOUmHhsaR9n+UpVpIMrJkvaQ5utvB2sISjtRJSqQRV8ruAiIiIiCgr2FuKf258n7dI/l09ZW2+5N6vQjlaoCLmmqmFsnPdGCys1gVLKneATiozM5J5yRMkT0NikM8t6XlBwuQJEf2L23YRERFRtnX7dRTqzzuFg7cD8TQkBrMP3kdYrPEyf8D4ISlOrUt17PKv7mD5tmk4tmIIOt88bDZxctOzAIa3HI9ag5ZhVflWJhMniZ8P1Crkhjs/NUK3SrkxukGhVD9fkSyZopBJcWp8HewbUT3Va4iIiIiIPpYVvcojr6sNVqcotv7vwhNhlTgAWCpkOPd93VTHe+iWB0OHLsKcmj2hkokTMgq9DmPPrMffG75DrvDANOf2NDQWsw/ex5lHIQDEL07V/e0Uzj8JFc5NlAkkoq8UV54QERFRtmHuOWeD3wv4v4hAtEqLJSefYE77kuhY3kfUR5biYqkESLmLlsSgR50nVzDk4jZUeH031bkczV8Byyq2hZ+Pb7o2Tna3swAAWMjNvzm3rGd5DFh7JXEuKdoUJmqcEBERERF9KvWKeqBeUQ+juAFC9kQkh6NVmmPKLRXCKpRf/1mAkkGPRe3l3tzHgVUjML1uf2wu1SjV791LTj7BkpNPsH1IFchS9Nt1/bVwzG27iOg9Jk+IiIjoqxCdrHj8+G030aq0N3b7vxFiKq0ef19+iTpF3OFmZwGZVAK9LvFBT67Tovn9Mxh8cRuKhD43+xkqmRw7i9fF8gqt8dg1V4bmV9TL3iimlEmh1iUVg69ewDVDYxIRERERfS4crBQZ6m8hl2Jys2Lov/ZKYi2U7r9ixPnNGH7hb8gMSd+RbTQJmHVoEeo9uYQJjUcg1MYp1XHbLbmAvK7i+oCGZC9NJV95otcbIOVSFKKvFpMnRERElG2Y25/YVPybTf44eCdIOD//5B3OP3kHAHj0SxPo9AZYahLQ8eYRDLy0Ezmjgs1+boSlLdaVaYa1ZZsjxDb1hzVzbC2Mv5at61cR322/KRS9T15k0/XflSpERERERJ8zL/vEFSZlfBwxoEZe5HKxMerjbmeBukXcsfnySzQt4YlFXcpCo9cjOiHpBSitTI75NbrjVL5ymLdvHvJEiLfravD4EsqsHI7vG4/E0YKVUp3Ts9BYs23vnx2uBISh96rLmNisKLpUzNiLUUSUPTB5QkRERNmKuZomKSVPnKRUbsxWDL22D32u7IFLfJTZfq/t3LC8YmtsKdkQccq0tx14z8FKgZH1CsLOUo7x224CAKyVxtt1VcrngpPj6gjnMqkER0bXhFqnh71lxt7cIyIiIiL6lDYOqIRlp58KLwJJJBJMbFbMZF8DgKkti6ORrycq53WBVCqBhVQGlVxv1PdajqJo2ud/mHR8BbreOChqc42LxPId07G5ZENMqzcQ8UrzhelTfv577xeaDNlwDTEqLSbsuIUJO25hSbeyaFLCK13jEVH2wOQJERERffZOPQyBrYX5WiDvSQDUmnvCZDw9PKJD0e/ybnS9cRC26niz/R665MKfldthT9Fa0MqMv06Nql8QdYu4o+WicyavV8ql6Fc9LwAIyRMrZfq+lhX0sEtXPyIiIiKirFQ1vyuq5k/ftrMGQ2IR+TqF3UVxpZm6fnFKK/zQeDiOFqiI2Qf+B7e4CFF755uHUeHVXYxoOR53PfKl6/PfexmW+Byg1YkTN0M2XEPArGbpuBsiyi6YPCEiIqLP2tuoBPRaeckovsHvObpVym0UT760P73yvXuFgZd2oO3t41DqzV9/zbsw/qjcEccKVIBBYr5Au8EAlMzpiGuTG6Ds9CNG7aa2TU5PcoiIiIiI6GtiLnny3vECFdG47yLMOvg7Gjz2E7XlD3uFneu+xczafbG6XItUi8kn9zoiHo+Do6HVG9LuTETZGpMnRERE9Fl7G5VgMj5x523j5ImZ56FTD0NMxksGPsTgi9vQ+OEFSGH+4ehEvnJYUrkDLuUsbvahq7i3Pe68EW/x5WyjNNlXkmyivavmweE7Qehe2TgRRERERET0NUtPsfZ3No4Y0HYSOtw6ginHlolWkFvotJh67C/UCLiOcU1HIczaweQYBoP4WeD8k3fQMXlC9NVj8oSIiIiyjXS9S2YwoPLLWxh2/m/UeO5vtptOIsW+IjXwZ+V2uOee9lL/nlVy47vttxI/Io2+yZ8Bp7Ysjiktipktdk9ERERElP39x0SFRIKtJRvics7i+N/euSgZ9FjUXO/JZRxYNQKjmo/BhdyljC4PjxPXTfS0t4RWx+QJ0deOyRMiIiL6LKw69ww5HK3QsLjnB4+RagLCYECtZ9cw/PwWVHh912w3lUyBv0s2wF8V2+KlY/rnoki+pYAh9QetlIUymTghIiIioq+Zt6NVpowT4JwD7brPxdjT6zDo0g5Rm0dMGDZsnoQlldtjfvVuotqFJx6IV6rrDQZo9cbF6uccvI8uFXPBx9k6U+ZLRJ+31DcOJCIiIvoEbr2KxLS9dzFw3dUMXTdi03VExmuE85TL7QFAYtCj0cPz2LN2NNZsnWI2cRKltMbiyh1QbchKTG44NEOJEwCwsUh6+Eq+wv/P7mVF/a5NboBmJb0yNDYRERERUXa0ZWBl1Crkhv91LpOu/l4Olmn20cgUmFmnL3p2mIYQa0dRmxQGDLu4FVs3fIecEUFmxxi8/hpM7dr1x8kn6LT0QrrmSkRfPiZPiIiIKEs9Do7G8rNPzbantohj7403WHwiaUm+JtnSepleh5Z3T+LgyuFYunOG0dL994JtnDCzdm9UG7oKc2v1QqiNk9CWw9EKOZ2S3oL7o1tZU0MAAOoVcU+ac7JtBxr7emFay+LCubk6KEREREREX5tK+Vywpm9F5HG1MdunTmE3WCtl8P+xAVqXyZHusU/nK4cmfX/HqbzG3+HLBD7AP6tGotGD8xme85tI0zUZiSj74bZdRERElCaDwYDvtt+Eu50lxjYqnKlj1593+j9dHxKtEo4TNDoodBq0vnMCQy9uRd7wQLPXvbJ3w5+VO2BrifpQyU0nNKISNDj7XV1svfISHvaWaFrCC/M6lsK3f98Q9WtbJgfkMvPvpHStlAtSCVAlv2sG746IiIiI6Ou2sncFqHV6WMhlSEf9eJFQGyf07jAV/S7vwvhTa6HUa4U2e3Uclu6agRXlW2FW7d7QyBT/ea56vQFhcWq42lr857GIKOsxeUJERERpevA2Gn9feQUAmZo8+fvKS7Ntb6MSEBarNtv+3tXn4QAAC60arc4fQK+zfyNnVIjZ/s+cvPBH5Y7YWbyOaJ9jU6ITtHCwUqB/jaSC8TITT2wpF8ekXC2jkEnRo0qeVD+LiIiIiIiMSSQSWMhlAADZB9QKNEikWF6xLfx8SuB/e+cYvWDV78pulH19H8Naf4c39u5mRkmffmsu48SDEOwcWhVlcjmlfQERfda4bRcRERGlSaUxLpb4oRI0OgSExgIAxm+7abZfpRnH0GThGbwMj0t1vNCgd+h/aQfO/NkPE/9ZbDZxct81N0a2GId6/f/E1pIN0kycAEA+N+PtA6TJHtiq5neBXCrBsDoFRH1SLxdPREREREQfQprRpSfJ3PIqiOa9FmJXsVpGbWUCH2D/qm9Q+8nl/zI9ofD8uovP/9M4RPR54MoTIiIiyhC93vCfHlpaLz6H+0HR2DKwssl2g8GAx8ExwvndN1Em+9knxKDntX3oe2UPnONN9wGAm54FsKhKJxwpWAkGScbeG+lWKbdRLHnyZHprX+RwtIKlQpahcYmIiIiIKOOkH7DyJLlYC2uMaj4Wfj4lMPXoUljoNEKbU0I0Vm+bhsWVO2Beje7QSc1/x2/7xzm0LZsT3SsbPy8AgPw/PC8R0eeDyRMiIiLKEJ3BACnMPwwERsYjJkGLgh52JtvvB0UDAHb5vzbZrjcAwzZeE85TJiYc4qPR7/Iu9L66F/Zq86tSLucohkVVOyUWiPzAhyxrpfEDU/LSJgqpVDS/QTXzYef11+hbLe8HfR4REREREZmX0ZyEu50FrJQyPH+X7LlBIsGm0o1x06sgFu+ahTwR4m28hl3civKv72FEi3EItnMxOe61FxG49iJCSJ7o9Ab8uPu20C6TcrMfouyA/yUTERFRhuj0qW9KVWXmcTSYfxrBUQmp9tOb2QlMbzDgRVjSw837Je+O8VEYc3odzv7ZFyMvbDGbODmTuzQ6dZmJDt1m41S+ch+cOAGAwp7GCSBJsvFkMvHYE5oWhd8P9eBmxwKRRERERESZLaMr4KUSCdb3q2Sy7Y5HfrTovQD/FKpq1Fbp5W3sX/0Nqjy/ka7P+edWIDb4vRDOZfzFlShb4H/KRERElCH6lNXQzXjwNjrVdoOZyiA6vQGV8ia94aUJDsHY02tx9s9+GHFhC+zU8SavO1KgIlr3+A09Ov8Mv1wl/lPSBADGNy6MsiaKPCYvUmlqOb7kP34uERERERGZlvy7+Ky2JVAxj7PJfu9XkFfM6wwfZ2uz40Vb2GBo6wmYWm8g1FLxBj1ucRFYv2UyBvptB9J4BrrxMkJ0LufKE6Jsgdt2ERERUYaktfIko/1SehISgyKedrjp/xj9L+9Cr2v7YGsmYaKHBP8UroY/qnTEXY98Jvt4O1jiTaTpVTDeDpaY26EULBUytFtyXtTWqbyPyWtck60qkXEvYyIiIiKiT6ZeUQ/MPHAfnvaW6FwxF9qXy4kYlRalfzoi6rd/ZA3sSu92uhIJVpdvCX/vwli0exZyRoUITTKDHj+cXIWSgY8wvuk3iFNamRxCrRMvq+dzAlH2wDQoERERZcilZ2Fm2wzJ3shKnjwJi1Ujz/f7MWjdlWR9TY/RfdZ+FFwwA2f/7IdhF7eaTJzoIcHuorXQsN9iDG/9vdnECQDMaV8qtdtBtQKuyOlk/BBk7m2xPC7WyfrwoYiIiIiI6FMp4G6Lc9/XxYmxtQEAcpkUjtZK/NLGV9Qvr6sNRjcoBAdrBQDxd3hz/L0Lo1nv/+FY/gpGbc0fnMWutWOQN8y4bqNebzAqZM/kCVH2wOQJERERZUi/NVfMtiVfbJI8edJq8VkAwKE7b4VYytyJc1wkvj+5Cmf/7If2R9bDRmO8WkQnkWJXsVpo0O8PfNNyHB675kp1rt0q5YKDlUIUuz+9sdF8UyZBvk32oJWSo7US4xsXxoi6BeBorUz184mIiIiIKHPlcLSC1b/bcr3XrVJuKGTmExZ/9iiXrrEjrezQv91k/FqjO/QQj1fo3QvsXjMa9R/5CbEEjQ715p3C6vMB4nHiNND/+7Bx9lEo3kSYXklPRJ83bttFREREaTJX5+TYvbfQ6g1oVNwTALDw2COhLXny5GWY8cPC+yFdYiMw4NIO9Ly+H9YalcnP0Umk2FO0JhZV7YQnLqa300puUrOiaFMmB5xtlLgXmFR7ZUabErBUJD1oRSVoACS+sfbe6j4VULuwe6rjD61dIM05EBERERHRp2OpkEGj05psK+Jpn64xyuV2wtXn4VhUtTNuexTAwr1z4aCKFdrt1XFYvmM6FlbtggXVu+Dq83A8C401GmfLlZeI0+jQpYIPuq9ITLYEzGr2AXdFRFkpwytPTp8+jRYtWsDb2xsSiQS7du0S2jQaDb777juUKFECNjY28Pb2Rs+ePfHmzRvRGLVr14ZEIhH96dy5s6hPeHg4evToAQcHBzg4OKBHjx6IiIj4oJskIiKi/yZl8uRyQBgSNDr0W3MFg9ZdFZIQ/0uWPAmNVac65uuHzzHhxEqcWdoPgy/tMJk40Umk2FG8Dhr0+wOjW4xNV+IEAIp7O8DF1gISiUT0Blp+NxtRvzi1DgBEfXKlUlCSiIiIiIg+Tym3zkpLj8q5jWJlczkKxyfzl0eLXgtwzy2PUb9vzm/Cim0/wSYu2qjtvb033uDi03dm21eefYY1KVasENHnJcPJk9jYWJQqVQqLFi0yaouLi8O1a9cwefJkXLt2DTt27MDDhw/RsmVLo74DBgxAYGCg8Gfp0qWi9q5du8Lf3x8HDx7EwYMH4e/vjx49emR0ukRERJQJUtQ/xHfbbuLso1DhPOHfJERyk3fdRki0SlQHBUhcaTLhxEqs/KkjBqWSNNlevA7q91+Cb5uPwVOXnBmar1Ke9OCUfL9hhTzxq0/JnA4AgFI+jgAy/qBFRERERESfl84VE1+0qpzP+YPHKOhhJxz/1Ko4Xjh5oW33X7GrWC2jvnWfXkGxlnVROCTA7Hh6M3Uew2PV+GnfXUzZcwdxatOrZYgo62V4264mTZqgSZMmJtscHBxw5MgRUez3339HxYoV8eLFC+TKlbQvubW1NTw9PU2Oc+/ePRw8eBAXL15EpUqVAADLli1DlSpV8ODBAxQuXNjoGpVKBZUq6ceXqKiojN4aERERpeD39B1ehscjh6O4oPrT0Fj0X5us9omZ3EOFX46iU/nEhxjH+CgM8tuBXtf2pro9167itfF7lU4IcM7xwfNWJNuGK3nhd+W/8eU9y2PdxefoXDHxu4mFXIqq+V0Qo9Iij4t4dQoREREREX3+xjQojMp5XVA+j1OafWe3K4GbryKN4u3K5kRItAoV8zojVpWY1IhXWmJU87G44VUIE4+vgNyQ9GaZ8nkAtq8fh9HNx+BIwcpG4xmSVXp8GhKDUw9D0LVSLiRok14+02gNAEspEn2WPnrNk8jISEgkEjg6OoriGzZswPr16+Hh4YEmTZpgypQpsLNLzO5euHABDg4OQuIEACpXrgwHBwecP3/eZPJk5syZmDZt2ke9FyIioq+JVqdHp78uAgB+aeObal+DAdCkXJ7yrwNn72H05d3oe2UX7NSmCyVqJVLsKl4Hi6p0/E9Jk/ckybI58mRbcin/XXnibm+JMQ2Tvk9IJBJs6F9JOCYiIiIioi+LUi5FnSKp1y58r1OFXPB/edMoLpNKMKxOYn1DrU6PmoXccO15OGJUWqwq3wp33fNh0e7ZcIuLEK6xVcdj2Y6fMadmT/xRuQOQ7HliycknwnHd304BACLjNehQPmk7YrWZ5ygiynofNXmSkJCA77//Hl27doW9fVJhpm7duiFv3rzw9PTE7du3MWHCBNy4cUNYtRIUFAR3d+O/7Nzd3REUFGTysyZMmIBvv/1WOI+KioKPT/r2RSciIsoODAYDlp5+ihI5HFCtgOt/Hu/h2xjhODoh9aXkh+8EITbF1l02qjj0vroXAy/tEBVZTE4rkWJn8bpYVLUjnjt5/+c5v6fWJc1FnnzbLpn5HUuZNCEiIiIi+nro08hZyGVSrO1bEbv9X+Obzf4AAL9cJdCi1wIs2TUTZQIfiPqPP70WhUOeY3yTkVApLBI/w8S2XQuOPsKfp5KSKsmTJ/eDovDPrSAMqpkPNhYf/Z13IkrDR/uvUKPRoHPnztDr9fjjjz9EbQMGDBCOfX19UbBgQZQvXx7Xrl1D2bJlAZj+AcNgMJj9YcPCwgIWFhaZeAdERERflmP3gjHrwH0AQMCsZum6Rq3V4+LTd4iM16Cxryc6/HkBRb3sMbNtCUTGa4R+/i8iUh1n8u47wrGlJgE9rv2DwX7b4BJvehvNxELwdfF71U544eSVrrmmlMPRCq8jTK9ksVIkfcVJXvMkeSKFiIiIiIi+XnqDmYIkKehSZECC7F3RuetMzDi0CO1uHxe1tbp3CnnC32Bg24l4a2f+hbYETVLCRK1NOm684AwAICpeg6kti6drfkT08WS4YHx6aDQadOzYEc+ePcORI0dEq05MKVu2LBQKBR49egQA8PT0xNu3b436hYSEwMPD42NMmYiI6Iv3KjwuQ/1VWh0qzzyGnisvYcSm69h86QX8X0Zg06UXACAqXHjwjumVn8lZaNXofWUPTi8dgIknV5pMnOghwa5itVC//xKMazbqgxMnAJDX1XRtkm8bFEIx76TvHslrnkiZPCEiIiIi+qq9fyRIuSrEQm76Z1JTq0dUciXGNB2NX2r3hT5FAchSQY+wZ+23KPXmgfGFJnRddhHaFFt3rT4fkK5riejjyvTkyfvEyaNHj3D06FG4uLikec2dO3eg0Wjg5ZX4A0qVKlUQGRmJS5cuCX38/PwQGRmJqlWrZvaUiYiIsoW0EgMrzz7DsA3XhC/m9wOjERarFtoDIxNE/VNuw2WOQqdBV/8DOPHXQEw99hfcY8NN9ttfuBoa9V2EUS3G4Vkm1DVJrm2ZxPGal/TCyHoFxY0Sk4dERERERPQVWd2nAnycrbBpQGJhd0OKlSeWCpnJ61L2E0gkWFapLfq2/xFRSmtRk0dMGP7e+D1a3TmR5rwCIxNw+lFIOu6AiD61DG/bFRMTg8ePHwvnz549g7+/P5ydneHt7Y327dvj2rVr2LdvH3Q6nVCjxNnZGUqlEk+ePMGGDRvQtGlTuLq64u7duxgzZgzKlCmDatWqAQCKFi2Kxo0bY8CAAVi6dCkAYODAgWjevLnJYvFERESUds2On/bdBQA09vVEi1LeRgXek18+YtN12Kaxx65Mr0Pb28cx8vxm+EQarxh970iBiphfvTvueuRL4w6MVSvgAgkkkEiAM49CzfarlM8ZE5sVhbON0qjNRpn0EORia9xORERERETZX+3C7jgzvq5wnnLbLiszyRNXu9TLBJzMXwFtevyGFdt/Qp6IQCFuodNg4b7fUDj0OebW7AmDxPw77Mm38SKiz0eGkydXrlxBnTp1hPP3Rdp79eqFqVOnYs+ePQCA0qVLi647ceIEateuDaVSiWPHjmHhwoWIiYmBj48PmjVrhilTpkAmS/pLasOGDRg5ciQaNmwIAGjZsiUWLVqU4RskIiL6WqR3R6pYVeJ2XBqd+T1+9954Y/5z9Dq0uHca35zbhHzh5vudylsW86p3ww3vD3/xoWIeF3xTvyDmHX6QavJEIpHAxdb0Q41cJsXVSfVhAGAhN/1AREREREREX5eU23HNaV/SZL/ahdwwrE5+LD7xxGQ7ADxx9UGrnvOwePcsVH9+Q9Q29OI25Al7g9HNxwiF5I3nYsCJ+8HimN7AbYeJsliGkye1a9c2v1wNqSxl+5ePjw9OnTqV5uc4Oztj/fr1GZ0eERHRV0uaYuXJ+ovP4WqrRGNfcV2RUw9D0KmCD7R68dtNqT0MAAAMBjR+eB7fntmAQu9emO12IVcJ/FajO67kTLvAobVSBjc7Czx/Z7peS9/qeVK9voC7LR4Hx6B2IbdU+5lLrBARERER0dcp+cqT+9Mbm922SyKRYFyjImk+L0Va2aF3h2mYdHw5el/bJ2pr+vA8vDa9w4B2kxBq42RiLkCf1ZdFMbVOD0tp4pym7rkDpVyKH5oWTde9EVHmyHDyhIiIiD5PyV9KevQ2GpN23QYABMxqhgRNUv2SA7eDsOfGG9hZpvNrgMGAGgHXMe70WpQMemy225UcRfFbje64kLtUuoa9PrkBnGyU+H77TaPkyYi6BTC6fqE037T6Z2QNxKt1cLBWpOsziYiIiIiIACD5+9/mEicZpZXJMbXBYDxwy4OfjiyBQp/0HFYm8AF2rhuLPu2n4LFrrhRzMX4ZXa3Tw1Ihw9uoBKGA/Kj6BWGt5M+5RJ9KpheMJyIioqyRvObJi7CkZERAaCyKTzkk6rv/ZmCq23a9V+b1fWza/APW/f2j2cTJDc+C6N1+Ktp3m2M2cWKqHMv7xEjKWi0DauTFN/UKihInRb3sja5XyCRQyqVMnBARERERUYbpUu7blUGDahnXdOxeOTEpsql0Y/TqMA1RFjaidp/It9ixfhyqBviL4inrrwDAvMMP0eWvi4iK1wgx7X+cMxFlDJMnRERE2UTybbuiEpK+YP956onRg0GcWgdtKsmTQiEBWLZ9OnauH4sqL26Z7HPPLQ8GtJ2EVj3n4WT+8qYzJP+qU9jdKCb7NzmSfHHJ/pHVMbFZMchl4q8ojX098XNrX+wbUR2/tPFFbhdrTG2Z9rZgREREREREpjjbKjPU/68e5dC2TA7hvEo+F6M+DlZJL3adz1MabbvPxUsHD1Efe1Us1mydgo43DguxqHit0VirzwfgwtN3+OdWkBDTaFlYnuhT4jovIiKibCJ5EiIyLil5YuqNqrOPQ+Fq4mHBJyIIo89uQOs7JyGF6eTKE+ccmF+9G/YXqQ6DJH3vYchNbL8lF5InSW3FvR1MXi+RSNC9cm4AgG8OB3SrlDtdn0tERERERGTK2IaF8SYiHh3K+aSrf8PinmhY3BPjGxfBo+BoVC/gatTH1kK8Kv6xay606fErlm3/GWUCHwhxhV6HOQf/hzwRbzC3Zk9M2XPH7Ocmr1WZnt0DiCjzMHlCRET0hTIYDDj7OBSzD97HrLYlRUmIB29jhGNzK7t3+b8Rjt1iwjDi/BZ0vnEISr3xW08A8MbOFQurdcG2EvWhk2ZsT2CFzDjJ8n66aZQ1ISIiIiIiynTONkqs7lMxw9d5OljC08ESAFAxrzMuPQsT2nI4WRn1D7VxQucuMzBv/zw0e3BO1Db04jbkCg/CmGajoVJYmPy85M9Saq48IfqkmDwhIiL6AgVFJqDa7OPCqpIeK/xE21jdfRMpHJsqPviefUIMBvttQ58re2GlVZnsE2Zlj8WVO2B92WZQyTO2tP09uUycIalbxB0W8sQETMqaJ0RERERERF+C37uUQaUZx4TzZiW8cOFJKDZdeinqp1JYYHir7/Di1FoM8dsmamv+4Cw8YsLQv91kRFrZGX3GvCMPhWO1jskTok+JNU+IiIi+QL8ffyTajis82TZdAHDjVVLyZKf/a6PrrdQJGHrhb5z5sx+GXtxmMnESrbTC/GpdUXPQcqyo2CZDiZNcztai86r5xfsBr+hVXjiWMnlCRERERERfIA97S9QrklTfUSaVYGbbkib7GiRSzK7dG983Gg5tiu2PK7y+i20bxsM7KjjVz9MweUL0STF5QkRE9JmIV+vwKjxOFItTa7Hj2itExKlFcZWJ5dp6MytMkocVOg16XNuH03/1x/jTa+GgijXqr5IpsKxCa9QctBwLq3dFjIW1UZ/3elfNYxRb1bsCjo+phQ7lcgqx9uV8UNTLXjhPvtqE23YREREREdGXylJpvKWxo7XCRM9Em0s3Ru8O0xClFD9nFXz3EjvWjUXhkACz16q1euy49gqLTzz+4PkSUfoxeUJERPSZaDD/FKrPPoFHb6OF2KSdt/Ht3zcweP1VUV+tiTeOUnsJSarXoc3t4zi2bDCmH/kTbrERRn20Eik2lWyI2gP/wi91+yPc2nTx9uT6VMuD7pVziWI1C7lBLpOieSlvISaTStC2TA6TYzjZfNhWYERERERERFnNWmGcPDk1tg52D6tm9pqzecugQ/c5CLQVr9D3jAnD1vXjUfnFTZPXaXR6fPv3Dcw99AD3g6L+28SJKE1MnhAREWWBl2FxqPPrSay/+FyIvQqPBwDsvxWIay/CodMbsON64pZbF5+Gia7X6IxXmehNVYY3GFD7yRXsX/0N5u+fh1yRb03OZ1+RGmjY7w9MaDISgfZu6b4PCST4uXUJ3PixITzsLdCubE7I/l1KUjmfM/K52qBRcQ8AEOIp9amWB3WLuGNOO9PL24mIiIiIiD5XoxsUgrONEkNr5xdiDtYKlPJxxIUJdc1e98AtD9r1mItHLj6iuL06Dmv+/hFN7581uuabzf7C8eZLL0Uv3hFR5mPBeCIioizw0767eBYai0m7bqN75dyitgVHH2HB0UcYVie/KG4wGITtrkztdatLsW1XycCHmHByFaq8uGV2HifzlsPcmj1wx7NAmnPeOKASui7zE8W0+sR5OFgrcOH7epAmS5BYyGU4+m0tvN+hy1zyxFopx8reFdL8fCIiIiIios+Nt6MVrkysL3oWes/LwQpyqQRaUy+6AXhj74723eZg+fbpqPD6rhC30GmxaPds/BQThtXlWwrx1xHxwvHq8wFYfT4AN6Y0hIOV+W3CiOjDMXlCRESUBeLVujT7LD7xRHRectphzG1fEo19vUwmT8L/rYuSO/wNxp1ai+YPjN9Ueu9KjqKYU6sXLvn4pjqHEXULYETdgpBKALlMiknNiuLn/feEdm9HK+HY1MNC8pipdiIiIiIioi9das865hIn70Va2aF7p+n43965aPToYtKYMGDqsb/gGR2K2bV7wyAxvYHQuxgVkydEHwm37SIiIsoCl56Jt+EymCn2nlx0ghbDNl4HAJjYtQsrt1/EtCNLcHT5ELOJk/uuudG33Y9o321OmokTAOhRJTeUcinkssSvDP1r5BPaWpbyhqWJ/X3NkTN5QkREREREX5mKeZzT7KNSWGBI6wlYV6apUdvgSzvw6/75kOu0Jq9VyPjzLtHHwv+6iIiIsoA6xcqRDX4v0nWdBMD2q68Qp0r64mytjsc3Zzfi5F8D0evafij0xqta3ti5YmzTUWja5384XqAihL200uBma2G2zcU2Y4XeGxf3hFwqQdX8Lml3JiIiIiIiygb+6llOdG6jNP0CmouDNXb2m4C5NXoYtbW7cwJLds2EhVZt1KZLY2ULEX04bttFRET0GUhv8kSrN2DM1hsAALlOi843DuGbc5vgFhdhsn+khQ0WV+mINWWbQ6VISoTUKeyGEw9CRH2drBWY2KwY/J6+g1QiQUkfB6HGiilKecbewXCyUeL2tEZQ8s0oIiIiIiL6SjhaK9Gvel6sOPsMACA184zlbmeBHcOqo6tSjnG2zph58HfIDUkv3TV47IdVW6diQNtJiLWwFuIpa18SUebhrxdEREQfwd03Udjo9wL6dL4FlKEtrQwGNL1/FkdWDMHPR5aYTJyoZAr8WbEtagxegb8qtcO41qVF7ct6lje6xtvRCu3L5cTcDqUwu31JdKuU26hPchby9G/Z9Z6lQsbaJ0RERERE9FUZVDMfXGyUGFAjb+J2AiZMbFoUACCTSrC1ZAMMaDcZCXLxav+qL25i4+aJcIqLFGI6vQGH7wSh1twTuP4iXIjfC4zCBr/n6X4mJSJjTJ4QERF9BE3/dwY/7LyFf24HZuq4lV/cxK51Y/DH7lnIG248th4SbPWtjzoDl2JWnb6IsrQFAJTL7ST0uTSxHuQyKX7rUEp0bTp38hJ42ltm/AaIiIiIiIi+Mu72lrg8sT4mNitmLneCqgVcASS9WHcifwX06PgTopTWon6lgh5hy8YJ8IgOBZCYPBm47iqev4vD0A3XAADRCRo0WXgGE3fext6bbz7OTRF9BZg8ISIi+oiGb7yOtRcC0uxnQOpvAxUOCcDKrVOxedMPKB340GSf4/nKo0nf3zGu2Si8sXcXtZXJ5YS57Utiy8DKcLdLTHq0K5dT1Edi9mu82PxOpdC+XE50KJ8z7c5EREREREQkrMCvmDepgLyzjXEdSZk06efayz6+6NJ1JkKtHUR9Cr17ge3rxyN3+BtRzZPAyATsuv4avx56IMTuvonKtHsg+tqw5gkREVEGqbS6DG1Z9ePuO+hZJY9wbmrZdFBkgslrPaNCMebMerS7fQxSMwkWf69CmFW7Ny7mKpnqPDqU9zGK/T2oCjouvQAAqFvE3ajdlDZlcqJNGSZOiIiIiIiIMmpO+1IoO/0IAGDzwMrYd+MNGhb3FNpTbul8xyM/OnSbg/WbJyFHdFLdypxRwdi2YTymOioAiZsQH7XFH/lcbYTz1OpYElHqmDwhIiLKgKvPw9BuyQV0ruCDKvld0LSEFxQpCqAbUinYFxKtQt/Vl43ioTFq0bmNKg6D/baj/+VdsNKqTI711Mkbc2v2xIHC1TK+59a/KuZ1xsUJ9XD2cShalPL6oDGIiIiIiIgofZxtlLg1tSEi4zXI6WSNbxsWFrWbKgD/zDkH2nefg/VbJiN/2Csh7hYbgRkLhyOw/VRcy1lUiD8NjRWO9954g28bFIJSLhWeVZlQIUofJk+IiIgyYMqeOwCAzZdfYvPllwiOUmFAzXyiPnFqndnrFx1/hFuvI0Wx/TeTapfI9Dp0unkYo89sMFkIHgBCrB2xsFoXbC7VCFrZf/+n3NPBEu3LcSUJERERERHRp2BnqYCdpcJkm1qrNxkPtHdDx66zsGbrFPi+fSLEHVSxWPf3ZPRv9yMu5DbejeB1RDw2+D2HXCrB5N134JvDHnuGVRe2ESMi81jzhIiIKAOkKd7QOfUwxKhPrEprFFt7IQAqrQ4JGuMvwsM2XgMMBtR+chkHVo7AjEOLTSZOYhWWmF+tK2oNWob1ZZulmTixs5DDRinD8p7l07grIiIiIiIi+hxodMbPjN83KQIAeGfjiC5dZsDPx1fUbqNJwKptU1Hj2TWTY156FobJuxNfBLz9OgqvI+IzedZE2ROTJ0RERBmQcnmzUi7+p3SD33O0XHTO6Lofd99Bo/mnTY5Z7O1TrN8yCau3TUOhdy+M2nUSKdaXboJag5ZhYfWuiFNapWuuzUp64dbURqhfzCNd/YmIiIiIiChrmUqeDK6VXziOtrBBzw7TcCx/BVEfS60ay7f/hLqPLxldX8DdVnTOVSdE6cPkCRERUTqERKvQb/Vl3HgZIYorZOIvnRN33kZQlOni7wHv4rDlykvh3DMqFHP3L8C+1d+g+vMbJq85lr8CGvVdhEmNhiHUxsmovYinndk5S6USfikmIiIiIiL6gqh1pmto/tSquHAst7HG4DY/YH/haqI+Fjot/tw5A40enhfFfz/+WHTOp0Si9GHyhIiI6F8Xn77Dt1v8ER6rNmr7ef9dHLsfbBRXymXC8bUX4en6HBtVHL49vQ4nlg1Ch9tHIYXxl+M77vnQtdPP6Nd+Ch675jI7VvtyOTGzbQmTbXImToiIiIiIiL4omhQ1T2T/Ptf1rJIH+0ZUR5V8LljfvxI0MgVGthyPXcVqifor9Vos3jULze+Z3vkAAHR60wkaIhJjwXgiIqJ/df7rIgDAAGB+p9KitrdmVpMkX3my9NQTk33ek+l16HjzCL49ux5usREm+wTaumBurZ7YWbwODJL0veNgLkUiY/KEiIiIiIjoi+Jub4G7gUnnCzuXFo59czhg08DKwrlOKsO3zb6FRqpAh9tHhbjcoMfCvb9CqdNgh289o8/QpkieGAyJ5ym3qSb62jF5QkRElMLT0FisOR+AywFhmN+pNBQyKSRmUhRnH4Xi3ONQ3A+KhrXSzD+rBgNqP72CH06sMlnTBABilFZYUqk9VlRohQSF5QfPfXLzYpi+7y4AoHoB1w8eh4iIiIiIiD69WW1LoveqS2hVOgd6Vc1t/jnzX3qpDOObjoRaLkc3/4NCXGbQ49f9C6DQabGlVCPRNTp90uoWrU6P1n+cg7udJVb2FtdRIfraMXlCRESUgk6vx5Q9dwAALUt5Qy6T4MLTdyb7Bker0G25n9mxir19igknVqLGc3/TnyWRYlOpRlhQvavJmiZpMaRYbd2vel408fXEg7fRqF3ILcPjERERERERUdbxdLDEwVE1M3SNQSLFxIbDoJIp0ffqHiEuhQGzD/4OhU6L9WWbCfENfi8wpUViDZW7gVG4/ToKQBQMBgNXnxAlw+QJERFRCnFqnXAclaDF2K2mi7mnxj36HcadXod2t4+ZrGkCJBaDn1m7T6o1TdJiMDG2t6MVvB2tPnhMIiIiIiIi+sJIJPip3gCo5QoM9tsuavr5yBJAIsH6Mk0BAKvOBQjJk+RbeKl1elgkq+tJ9LVj8oSIiCiFwIik+iYZTZxYaFQYcHknhlzcBhuN6Topd9zz4Zc6fXE+T+n/Mk0AQE4na0TFa/7zOERERERERPSFk0gwq1ZvqGQKfHN+s6jp58N/JO58ULoxAOBKQBhi1TqM3HRd6KPSipMn0QkaWClkkMvSV4+TKLth8oSIiCiFeI0u7U4pGQxoce80vju1GjmjQkx2CbR1wa81e2KHr+li8NUKuODcY9Pbg6VUs5AbKuR2QuPinth69WXG50tERERERETZj0SC+TW6Qy1TYNyZdaKmmYcWQS+RYEupRmj/5wWjS1UaPWAJ6PQGLDn5GL8efoiC7rY48m2tTzV7os8K04ZERET/Uak3D7Btw3j8vneuycRJjNIKc2v0QJ2BS7G9RD0YJFKUyulg1C+3i026P7NSXmeMqFcQUin3oyUiIiIiIvraDKqZT3TerZJ4O+jFVTvht+rdjK6beXAROtw8bHJMlTbxRcItl1/i18MPAQCPgmMyY7pEXyQmT4iIKFuKStDg9MMQaHX6VPtdfxGOJSefQKc3XZckNR7Rofht32/YvW4Myr++Z9RukEiwu3wT1BnwFxZX7YQEhaXQVjGvs1F/a0X695bV6pLm65vDOBFDRERERERE2deEpkVx9rs6wvmAGvmwd3h1UZ/fq3XB/GpdRTEpDJh94He0u3XMaEyVNvH5+fqL8I8wY6IvD7ftIiKibKn7cj/cfBWJ75sUweBa+YV4gkaHzn9dRPncTmjs6yksVXa2UaR7bEtNAgZe2onBfttgrVGZ7HMhVwlEzZiNzbFOCHlqvBVX27I5sezMM1HMWilDpbzO8HsWBgCY1KwocjpZIzAyHr8eeoDYZIXs6xV1F46LeztgY/9KLBJPRERERET0FXG0VorOLRTG78kvrN4VUoNeVANFCgPm/rMAeokEO33rCnGVJjF58gHvFhJlS1x5QkRE2dLNV5EAgJ3XXovih+4Ewf9lBJaffSba43XdxedpD2owoOXdkzi+bDC+PbvBZOIkwNELA9tMRJfOMxBTpAQaFfcw6jOpWVHYKE28vyCRYG2/isKptVKOxr6e6FMtL25ObQQvh6SVKylXm1Qt4Io8runf9ouIiIiIiIi+bMoUhdxlZrZ1nl+9GxZV6SiKSWHAr/8sQMu7J4WY+t+dG0JixM+6H7JTA1F2wJUnRESUrUlSfHd8/yZNSrdfR6U6TpnX9zH5+DKUffPAZHuU0hq/V+2MNeVaQC1PXMWikEthb2W8osXOUg5LpYn3FwwGWMiTtu7SGZK+oMqkEihkfOeBiIiIiIiIEinlUjQo5oHoBA1yu1jj+bs40x0lEvxaowdkej2G+G0TwjKDHvP3zYNOIsP+ojWg0ujwLkaF0w/FtTzVWj2slOnfZpoou2DyhIiIsjVpiuyJ3pCxN2a8okLw3anVaH33lMl2nUSKzaUaYl717nhn4yhqU0glyOFobXSNrYUC7naWKOxhhwdvo5PNLfF/25XNiTOPQtCylLd4PBmLwxMREREREVGSZT3LC8ce9paitjntS2L8tpuJJxIJZtfqBalBj0GXdgh9ZAY9Fuz7FfEKC3T6C1jVu4LRZxy591b0fLr63DOExKgwrlGRTL4bos8LX2ElIqJsLVqlwU977+Lmqwj0X3MZvx42vXIkJSt1Akaf2YDjywabTZyczV0KzXovxMRGw40SJwAgl0lRNpcTFnYujSOjawrx0rkS+3as4GNy3N86lsKFCfXgkGLVCleeEBERERERkTlWShmmtigmnOdMWRdTIsHM2n2wvHwrUVih12HJrpmo8vwGAt7FGo07ctN1qLVJuzhM3XsXi088wePgaKO+RNkJV54QEVG29jIsHivPPcPKc8/S7gxAYtCj9Z2T+O7UanjGhJns88zJC7/U6Y+jBSoa7wuWjJeDJSQSCVqVzgEA+LN7OegNBuT49wusIZVVMKb2qvV2tML9IH45JSIiIiIiItO6Vc6Nm68jUTmvC5Ry4xfwprf2xWT0h1yvQ+9r+4S4hU6D5dun40L9ogCURtclaHVQyqXQJ6t/EqvSfZR7IPpcMHlCRET0r1JvHmDq0b9QJtBMXRMLGyys2hlryzWHRmZcyyS5Sc2KGhV1b+zrKTpPvoWYs40SPavmTnXMn1v7YuzWG+hTLW+q/YiIiIiIiOjrpJBJMa9jaQDAjZcRRu2uthaARIJp9QfCRp2ADrePCm02mgTUHNUbxdtPxx2P/KLrFhx5hB9bFINGn7QCJZV3CYmyBSZPiIjoq+cWE45xp9eg462jJtt1Eik2lG6CBdW7IszawWSf5Nb0rYhahdzS7JfP1VY4vjyxvsnVJsl5O1ph44DKaY5LREREREREZGrliZNN4qoSg0SK75qMgJUmAc0fnE26JiYKa7dMRseus/HENWmr6ZXnnmFso0J4F6MWYhIkPsMaDAb879hjFPGyQ6Pi4pcGib5kTJ4QEVG2ExmnSVc/hU6D3lf2YuT5TbBTx5vsczpPGfxctx8euuVJczyZVIIbUxrC1iJ9/7zWK+qOn1oVh28OhzQTJ0REREREREQZYapupqN10i4KeqkMo1uMgZVWhXpPLgtxl/gobNgyER26zcFLx6RkSJe/LuLGq0jh/P3Kk9OPQjH/6EMAQMCsZpl9G0RZJsOVZ0+fPo0WLVrA29sbEokEu3btErUbDAZMnToV3t7esLKyQu3atXHnzh1RH5VKhREjRsDV1RU2NjZo2bIlXr16JeoTHh6OHj16wMHBAQ4ODujRowciIiIyfINERJQ9aXR6kzVD5hy8j1I/HU7z+tpPruDgyuGYeHKlycTJUydv9G33I3p2/Mls4qRrpVyic6kE6U6cAIBEIkHPKnlQNpdTuq8hIiIiIiIiSg+LFCtPGhf3hIOVeAtqjUyBoa2+x/lcJUVxz5gwbNg8EZ5RoUIseeIEAKbvuwsAeBNh+mVEoi9dhpMnsbGxKFWqFBYtWmSyfc6cOZg3bx4WLVqEy5cvw9PTEw0aNEB0dFKB21GjRmHnzp3YvHkzzp49i5iYGDRv3hw6XVKRoa5du8Lf3x8HDx7EwYMH4e/vjx49enzALRIRUXbxLkaF3f6vEZ2gQdVZx9Fx6QWjPn+cfJLqGHnCXmP5tmlYvW0q8oe9NmqPUVphRu0+aNRvMY6nUhC+cwUfjGtYWBSTcMNXIiIiIiIi+kx42FsKx7PblcDvXcvAM1nsPZXCAgPaTsJ1L/Ezbq7It9iwZRKc4iKNrgEAv2dhABJfbiTKjjK8bVeTJk3QpEkTk20GgwELFizAxIkT0bZtWwDAmjVr4OHhgY0bN2LQoEGIjIzEihUrsG7dOtSvXx8AsH79evj4+ODo0aNo1KgR7t27h4MHD+LixYuoVKkSAGDZsmWoUqUKHjx4gMKFC5v8fCIiyn4SNImJdUuFDP3WXIH/ywhUzOuMkGgVQqJVeBAUjcKedmmOY6OKw/ALf6Pf5V1Q6rUm+2zzrYfZtXohxNY5zfGKeNpBJhMnS7jzFhEREREREX0ulHIp9g6vjluvI9GxvI/wwp9SLoVaK054xFpYo1fHadi8aQKKBT8T4vnDXmHVtqno2nkG4pRWRp+x8/oraHTGu0IQZQcZXnmSmmfPniEoKAgNGzYUYhYWFqhVqxbOnz8PALh69So0Go2oj7e3N3x9fYU+Fy5cgIODg5A4AYDKlSvDwcFB6JOSSqVCVFSU6A8REX3ZdHoDyvx0BKV/OgytTg//lxEAgEv/vt0CAN2W+6U6hsSgR9vbx3B8+WAM8dtmMnHi71UQrXv8hrHNRqcrcQIkFtmTpVhp0rSEV7quJSIiIiIiIvoUSuR0QNdKuUQ7JZh77y/K0hY9Ok7HE+econjpwEf4c+cMKHTG9UVHb7nBbbso28rU5ElQUBAAwMPDQxT38PAQ2oKCgqBUKuHk5JRqH3d3d6Px3d3dhT4pzZw5U6iP4uDgAB8fn/98P0RElLUi4tSI1+iQoNEjIt50EfjQGBUA4GVYHPR68dsuJQMfYvv6cZi3fz48YsKMrg2xccTYpqPQpsdv8PfO2KpGJ2ulqMj7kNr5Mb2Vb4bGICIiIiIiIvrUfutYymzbOxtHdOv0M17Zu4niNQOu49f9CyAxGG/RdePfFx2JsptMTZ68l3LPd4PBkOY+8Cn7mOqf2jgTJkxAZGSk8Ofly5cfMHMiIvqcJP8730RteMGmSy9QY84JTNlzBwDgGhuO2f8sxK61Y1D2zQOj/hqpDEsrtkWdAX9hW4n6MEjM/3M4vE4Bk/HK+VxgIZeiXhF3VM7njPGNCsMmA8XiiYiIiIiIiLJC85LeuD2tkSimTFZcPsjeFb06/oQwK3tRn1b3TuHHY8uMHtCvPA//eJMlykKZmjzx9PQEAKPVIcHBwcJqFE9PT6jVaoSHh6fa5+3bt0bjh4SEGK1qec/CwgL29vaiP0RE9OUxGAyYeeAeNl16AUOyL2QGmM+ezDpwHwCw+dxj9Lu0E8f/GoROt45AauKak3nLoVHfxZhZpy9iLKxTnUuNgq4Y26gwbkxpiI7lxcuWlXIpJBIJVvSugM0Dq7BYPBEREREREX0xbJO9/PdD0yIo7i3+LfWJiw/6tJ+CWIW4wHyfq3sx7MLfZsc1pPbmI9EXJlOTJ3nz5oWnpyeOHDkixNRqNU6dOoWqVasCAMqVKweFQiHqExgYiNu3bwt9qlSpgsjISFy6dEno4+fnh8jISKEPERFlTzdfRWLpqaeYsOMWdMm24dp1/bXZazQ6PWo+vYqDK0dg8okVsFfHGfV55uSFvu1+RO8OU1G6fiVRW99qeU2O+z4h4mClwJz25pc1ExEREREREX1pVvepgO6Vc6FnlTxY2KmMUfsN78IY3OYH6BUKUXzcmXXo7H/Q5Jh65k4oG8nw/iIxMTF4/PixcP7s2TP4+/vD2dkZuXLlwqhRozBjxgwULFgQBQsWxIwZM2BtbY2uXbsCABwcHNCvXz+MGTMGLi4ucHZ2xtixY1GiRAnUr18fAFC0aFE0btwYAwYMwNKlSwEAAwcORPPmzVG4cMb2pCcioi9LvEYnHKt1SXupzvjnvsn+OSPfYvKxZWj06KLJ9hilFX6v2gmryrWCWp74ha9Kfhe8iogXCs//2KIYVp57ZnRtyrUkrUp7Y7f/GzTx9czILRERERERERF9dmoXdkftwol1p3O5WOP+9MYoMlmcFDmTtyywajXQvZso/svhPxBuZY9DhcUvuuv0BlF9UKIvWYZXnly5cgVlypRBmTKJ2chvv/0WZcqUwY8//ggAGD9+PEaNGoWhQ4eifPnyeP36NQ4fPgw7OzthjPnz56N169bo2LEjqlWrBmtra+zduxcymUzos2HDBpQoUQINGzZEw4YNUbJkSaxbt+6/3i8REX3GDt0Jwq1XkcJ5dILWbF8LrRojzm3C0eVDzCZOtvvWxdI/92NppfZC4qReEXe0Kp0D3zYoJOo7rE5+AMDAmvmEmK2l+B2DmW1LYEm3spjbgatQiIiIiIiIKHuxVMjQoJhxyQRpt65Y1v4bUUxm0ON/e+ei4svboriOS08oG5EYsulGdFFRUXBwcEBkZCTrnxARfSauvwjHP7cCMbpBIVgrxYmJl2FxqDHnhCi2eWBldP7LODFS58llTDn6F/JEBJr8nBueBTG1/iBcz1EER7+thfrzTgltAbOaCcd7brxBfjcbFPd2gE5vwP2gKBTxtMe2qy+x+vxzLO9VHjkcrf7LLRMRERERERF9MV6GxeHMo1D8sPOWEAuY1QzNfz+DRpsWY8SFLaL+kRY2aNv9Vzxx9QEA3J7WSFRPhehzk5G8Af+fTEREn0ybP84DALR6A6a0KC5qC4xMMOp/4JY4OeITEYQfj/2FBo8vGfUFgHdW9phdqze2lqwPgyRxcWUBd1uMb1wYcw4+wMi6BUT9W5byFo5lUgmKezsAADpVyIVOFXJl8O6IiIiIiIiIvmw+ztboWikXVpx9iichsULcWiHHbzW6wyUuAl1vHBLiDqpYrNk6BW16/IYQWyesOvsMITEq/Ni8GOSyTC23TfTJMXlCRESfhD7Z0t1rLyJEbQ/fRuP77TeNrllz4TkAwEKjwhC/bRhycRssdBqjfjqJFOvLNMFvNXogytLWqH1o7QIYWruAUZyIiIiIiIiIjC3tUR4/7LyFb+oVBJBYK3TqnjuY1HAo3GIj0OCxn9A3Z1QwVm6bik5dZ+G3Iw8BAL45HNCxvE+WzJ0oszD9R0REme5BUDR+3ncXYbFqIbbz+mvhODo+MQFiMBhw900UGs4/jaehsUbjwGBA/Ud+OLJiKEad22QycXIlR1G06LUAUxoMMZk4ISIiIiIiIqKMKeBui78HVUG1Aq4AEpMh24ZUhV4qw4iW4+DvJa4jWuLtE/y+Zw5keh0A4HFwzCefM1Fm48oTIiLKdI0WnAaQuBXX4m5lAQDXXoQL7ZH/Jk/WXXyOH3ffMTlG7vA3mHL0L9R9esVke4i1I2bV7oMdvnWELbpSKubFmldEREREREREmSlBYYl+7X7EznVjkCvyrRCv9+Qyph35E5MaDoUkC+dHlFmYPCEioo/mxqsIaHV6SCUSGJLFY9VavI6IN5k4sdQkYOiFrRh0aTssdFqjdp1EirVlm2F+9W5prjQpl9vpv94CEREREREREaXwzsYRvTtMw/b14+CUEC3Eu/sfwGsHd0RWHoPbryMRq9Ji+7VX+KFpUThaK7NwxkQZx+QJERF9NBqdHg3mn4anvSXyuNoI8QSNHtVmHRd3NhjQ6NEFTD62HDmjgk2O55ezOKY0GIz77nnT9flyGd91ISIiIiIiIvoYnrrkxIB2k7Bh8yTRNtvfnVqDkfZuaO5XW4gZDMDcDqWyYJZEH47JEyIiylS/H3skHL+NUgFQ4VloLC48fWf2mrxhrzHtyJ+oGXDdZHuwjRN+qdMXu4vVBiSmEyItSnlj7403mNGmBIKjE7D1yisMqZ3/v9wKEREREREREaXiSs7iGN18DBbtng1psj0nft2/AG9tXeCXqwQA4Pm7OFx48g4P30ajZ5XckJh5tif6nEgMBoMh7W5fnqioKDg4OCAyMhL29tzznojoY9ly+QVWng3A8l7l4eNsjTzf70/3tVbqBIy4sBn9L+2CUm+8RZdWIsWq8i2xsFpXxFhYpzrWrakNEZWgRQ5HKwCJxej5ZYyIiIiIiIgo85h75u93aScmn1ghioVb2qF1z9/w3MkbFfM649KzMKHt7Hd1kNMp9ed8oo8hI3kD0xV2iYiI0um77bfw4G00RmwyvWrEJIMBjR6ex9HlQzD04jaTiZMLuUqgSZ/f8Uvd/mkmTgDARikXEicAmDghIiIiIiIi+kRWVGiNVeVaiGJOCdFYse0n2CfE4OarCFHbsA3XPuHsiD4Mt+0iIqJM4f8yAqvPPUuzn09EEKYeXYp6Ty6bbA+ydcYvdfphb9GaZrfoMkUqZbKEiIiIiIiI6FOxt5QjKuHflyElEkyv2x85I9+iweNLQp8CYa+waPds9OkwFZDKhPjriPhPPFuijOPKEyIiMslgMECr02fomun775ltU2o1GH5+M46sGGoycaKRyvBnxbao1/9P7C1WK92Jk8bFPTGyXsEMzZOIiIiIiIiI/pubUxuJzvVSGUY1H4t7bnlE8ZoB1zHl6F+imFafLStJUDbD5AkREZk0ZusNVPjlKMJj1SbbY1VaozadmS8/VQP8cWDVCIw9sx6WWuPxzuUuicZ9FmFWnb6ITWOLLjc7C9H5nz3K4dsGhVK9hoiIiIiIiIj+u59b+wIApv/7v+/ZKBNXlcRaWKN/ux8RYuMoau95fT96Xt0rnOt0Sb8fvC/JnU1Lc9MXjMkTIiIyace11wiP02D7tVcm20tNO4wy04+kOoZbTBgW7pmLjVsmIX+Y8TjBNk4Y2WIcunX6BU9cfdKc0+x2JdCtUq703QARERERERERZarulXPj1tSG6FE5tyg+qFZ+4fi1gzsGtpkElUwh6jPl2DLUfHoVQOLKk+svwjFu6w1Un30CD4KiUX32Cfx66MHHvwmidGLyhIiIUqXSGm/dpdMbUl1iK9Xr0OvqXhxbNhit7p0yvl4ixapyLVBvwJ/Yk4EtumwtFOhWKekLmqutMl3XEREREREREVHmsLNMSoq0Ku0NV1sLo2TK9RxFMK7pKFFMZtBj0e7ZKBD6AvEaHdr8cR5br77C64h4NFpwGq8j4rHoxONPcQtE6cKC8URE2cj7Ja6SDBRaT4up5Em8Rme2f6k3D/DL4T/g+/aJyXZ/r0KY2HAo7ngWyPBcJJLEbbvuTGuE3f5vULuwW4bHICIiIiIiIqLMsaBTaej0Bshlxu/o7ylWC/nfvcI35zcJMXt1HFZs/wmte/yGcGuHTzlVogxj8oSIKJswGAzoufISdHoDNvSvlGkJFI2JovGxKq1RzD4hBuNPrUFX/4OQwnhVSqSFDebU6oVNpRpBL5WZ/CwHKwUi4zVm51K3iDsAwMZCjq7cvouIiIiIiIgoS0kkEshl5n9/WFC9C/KHvULz+2eEWO6IIPyxexZ6dJwOrYw/T9Pni9t2ERFlE5HxGpx5FIrzT94hOFqVaeOq/1158io8Do0XnMbmSy/Qa+WlpA4GA9rePobjywahu/8Bk4mTbb71UHfAUmwo09QocdK2bA4AQJlcjtg0oLKozd3OAg2KeSBgVjM8m9kUlgrTSRciIiIiIiIi+vwYJFKMaToK/l4FRfEqL25h4okVWTQrovRhao+IiIz8vO+ucPw+eTL74APcD4rG9ztuCW0FQ57j5yNLUOnlbZPjPHTJhUmNhuKSj6/Zz5rXsTTmtCsJuUyKeHXSdmBV87tgbd+KkEkT32DJzK3IiIiIiIiIiChzre5TAXtuvMGOa6/hYW8BX28HHLsfDJXCAgPaTsaeNaPhFfNO6N/n6l7c8ciPbSXqi8b551Ygmpbw+tTTJzLC5AkREYno9QYsP/tMOH+fPIlXJ23VZaVOwMjzm9H/8k4o9Mb1T+IUFlhYrQtWlG+d6hLc7UOqAoCwN+r7RAkAfNe4iMk9U4mIiIiIiIjo81O7sDtqF3bHjDYlIJVIoDcYUGTyQQBAiK0zBrWdiK0bvoOFLmm77l8OLcYjFx/c8C4sxIZuuIaAWc0++fyJUuKvUkRE2YTBYPoYAO4HRWH71VdCQfnk4tRatF58DvOPPAQAqFPUODl67y0AQC5N/CejwaOLOLJiCIb4bTOZODlUsDIa9FuCpZXap7l3abncTqJzebLkiZQrTYiIiIiIiIi+OJYKGZRyKSwVMpwaVxtFvezRtkwO3PQqhAmNh4v6Wug0+HPnDLjFhGfRbInM48oTIqJsQpcsMaJPkSRpvCCxMJu9lQINinmI2rZffQX/lxHwfxmB0Q0KGRWIfxerxokHwbh54SaWHVmKBo/9TH7+SwcPTKk/CMcLVBRi2wZXQfs/L5jsLzWRG5EmC+ZwsjJ5HRERERERERF9GXK72ODANzUAADuuv8YO33oo/vYp+l3ZLfTxinmHJbtmoEuXGdDIFFk1VSIjXHlCRJRN6PXmkyfv3XwVAb3egPHbbmDyrtt4HByDOLV49cj7bbrek+l1ODt0Io4sH2oycaKWyrGoSkc06LdYlDgBgPJ5nDGwZj6TczG3suTk2No48E0NONsoTbYTERERERER0ZdrRp2+OJe7pChW/vU9TD26VDhPvnNGgkZn9FsF0afAlSdERNmEaOWJme8UOr0BZx6H4u8rrwAA6y4+x+j6hYT2kGgVtMkuLhH4CDMPLYLv2ycmxzufqyQmNxyCJy4+ZudlbvMtc8mTPK42ZsciIiIiIiIioi+bTirD8JbfYe+a0cgZFSzEu/kfxB2P/NhYugk0OgP8noVij/8bbL36Cq62SlyeWB8SbvFNnxCTJ0RE2USyhSeiREpyOoMBUfEaUWzNhQDhuMIvRzGjTQnYquIw5sw69Ly2HzKDcSYmxNoRP9fth93FagMf+MVlTvuSaXciIiIiIiIiomwn3NoBA9tOwvb142ClVQnxqUeW4r5rHmj1jdBjxSUhHhqjhlZvgELG5Al9OkyeEBFlE8m37dKZWXqi1xuMtvQKi1UnnRgMODVrKY4e/ROeMWEmx9hYqjFm1e6NKEvb9E3MxPeavcOro0ROh/RdT0RERERERETZzl2PfBjX9Bss2jNHiCn1WizePQsb91Q36q/TG6CQfcoZ0teOyRMiomwgOCoBY7feEM7f13zX6vSQy6Si+LXn4SbH8I4KxrQjf6LB40sm2x+45sIPjYbjas5iGZpbDkfjwu+2lvznh4iIiIiIiOhrt69oTRR/+xRD/LYJMa+Ydyg6dhCkHadDL03Kluj0BjwOjoangxVsLfi7An18LBhPRJQNjNt2E37PklaK6PQGrD73DAUmHkD7JeeFuN+zd1hz4bnoWpleh36Xdv5bEN44cZIgV2JOzZ5o3nsh7uT1Rd0i7kJbfrek+iQV8zrj2cymRtd3rpALXSvlwh/dygoxLrMlIiIiIiIiIgCw+202NLXriGLVnt/Et2c3iGLXX0Sg/rzTaL343KecHn3FmKIjIsoG7gdFic4fBUdj6t67AIAryVaa3Hkj7lcy8CFmHlyE4sFPTY57Ok8ZTGo4FC+cvAAAF76rC2ulDKvOBaBRcQ/kcLTGpYAwlMrpABsLOSQSCRQyCTS6pK3BlHIpZrQpAQAYWa8gYlVa5HSy/u83TURERERERERfvO7V8gF/bwHKlAFevxbiwy/8jevehXGsQCUAwPZrrwAAj4NjsmSe9PVh8oSIKBtIWR9+4s7bqfZ/XxC+19V9kMK4uHyIjSN+qjsAe4vWFBWEt1TIYK2UY1idAkKsViE30bV607XqAQDfNiiU6ryIiIiIiIiI6OtR2scx8cDNDdi6FZrqNaDQ64T2+fvmoVnvhXjp6InQGJXpQYg+Em7bRUT0BXsZFodOSy8gOFr8BSJGpTV9gcGARg/O4+jywehzda/JxMmG0o1Rr/+f2FuslihxAiBde4r2rpoHAFC/qEf6boKIiIiIiIiIsr2xDRNfqFzQqTRuTm2I6a2KY3mv8kkdqlTBz3X7i66xV8Xiz50zYKFRISpeI8R/3ncXY/6+AUPKt0mJMpHEkE3/HxYVFQUHBwdERkbC3t4+q6dDRPRRdFt+EecevzOKF/Oyx91A8RZdOSKDMe3IEtR/ctnkWGkVhLezlOPW1EZpzkmt1cPv2TuUz+0MK6Uszf5ERERERERE9HWIjNfAwUphtj3Pd/vwv71z0fLeaVF8c8mGWNN3Eu6l+K3j7Hd1uDU4ZUhG8gZceUJE9AULjjK9ZFWerCC7TK9D/0s7cGTFEJOJkwS5ErNr9ULz3gvNJk4AwMQiFZOUcilqFHRj4oSIiIiIiIiIRFJLnAAAJBJ833gEHrn4iMKdbx5G/fN7jbq3/eM84tU6ozhRZmDyhIjoMxUSrcLB20HQmSkiEhyVgEdmiqTdD4oGAJQIfIQ9a0Zj0omVsNYYJ1pO5S2LBv3+wJLKHaCRpfEFhoiIiIiIiIjoI3K2USJOaYXBrX9ArMJS1DZsx0IUDgkQxYKjVThy7+0nnCF9TZg8ISL6TDX//QwGr7+KjX7PhZheb8DkXbfRa+UlbLr00uy1srg4TDy+HLvWjUHx4KdG7SE2jhjRYhx6dZiGl46eZsdJXuPEzc7iA++EiIiIiIiIiCht3zcuAgB44uqD75qMFLVZatVYtHs2rNQJori4WitR5mHyhIjoM/X23y25Dt1JeoNix/XXWHfxOU49DMGGZEmV5Go+vYrDK4dhwOVdkBn0Ru2pFYRPTioBjn5bC90q5UJpH0cs6V7uP94REREREREREZF5CnnS7xT7itbEqnItRO0F373E1KNLRbERm67j9uvITzI/+roweUJE9Bnad/ONcGyAAQkaHcJi1dh2NWm1SXC0eBsu57hIzNv3G9ZunQKfSOMlqw9cc6Ftt7mY2Gg4oixtjdqr5HPBhQl1RTFPB0v80qYEdg2rhsKedv/1toiIiIiIiIiIzFLIxD9Xz6zdF7c98otinW4dQas7J0Sx/x179NHnRl8fedpdiIjoUxu+8bpwbDAA9X47hdcR8aY7Gwxoc+cEJh9fDuf4KKNmlUyB/1XtjL8qtRXVNcnhaCUa89eOpeDlYCWcmym1QkRERERERET0USRPntQo6Iozj0IxvOV47FszCrbqpN8wfjn8B254FUKAcw4AAH/CoI+BK0+IiD4TYbFqNF5wGhN23BLFtXqD2cRJzoggrP37R8zfP89k4sTPxxdN+vyOxVU7GRWE7101DzqV9xHO5VLuEkpEREREREREWcc3h4NwvLRHOYxpkJgg+aHRMFE/W3U8Fu+eDQutGgBgMDB9QpmPK0+IiD4TZacfAQDcD4oWxS89CzPqK9Pr0PvKHow5ux7WGpVRe5SFDWbU7oMtpRrCIDHOk//Sxhcdy/vgcXAMtlxJ3ApMxuQJEREREREREWWhHI5W2DSgMrR6PayVcgyunR+/HXmIPcVqo+rzm+h887DQt3jwU0w4sRJTGwzm7hn0UTB5QkT0GVhzPiDdfYu9fYpZB/+HkkGPTbb/U6gqpjQYjBBbZ5PtcqkE3SrlFo6Tx4mIiIiIiIiIslKV/C7CcfJtvKbWH4iyr++j0LsXQqz3tX24kLsk1IVb4U1EPMLj1Cju7QCizMBtu4iIsoAuxSsRU/bcSfMaS00Cvj+5CnvWjDKZOAmydcaAtpMwtM0PZhMnQOI2YO9JkuVL3q88WdCpNGRSCZZ0K5vmnIiIiIiIiIiIPoUEhSWGtfoO8XILUXzOPwvhFBKIqrOOo9n/zuJlWFwWzZCyGyZPiIg+sd3+r1Fi6iGcfBCc7muqBvjj4MoRGOy3HXKD3qh9XZmmaNB/CY4UrJyhuUgkyVeeJP6T0LpMDtz7qTGalPDK0FhERERERERERB/TI7fcWNflW1HMQRWLLosmQqrXAQDuBRrXhCX6EEyeEBF9Yt9s9kecWofeqy5j+ZmnuB9k/h91h/hozPlnATZumYQ8EYFG7Y9cfNCu2xxMbjgU0RY2GZ6LNFnyRJrsXwSlnP88EBEREREREdHnpX5Rdwxc8wv2FK0pild4eQeD/bYDSNzq6+HbaK5Aof8s038dy5MnDyQSidGfYcOGAQB69+5t1Fa5svhNaZVKhREjRsDV1RU2NjZo2bIlXr16ldlTJSLKcj/vv4fGC84YNxgMaHH3FI4uH4KOt44aNaulcsyv1hXNev8PV3MWE7XNbFsi3Z/vYZ+01FUuZcKEiIiIiIiIiD4vPavkhlImxelxdbC8VwVAIsGsVqPw0sFD1G/02Q0oEfgIUQkaNJx/GjXmnMiiGVN2kem/lF2+fBmBgYHCnyNHjgAAOnToIPRp3LixqM8///wjGmPUqFHYuXMnNm/ejLNnzyImJgbNmzeHTqfL7OkSEX1SS04+SbOPd1QwVm6bht/3zoVbXIRR+5UcRdG0z/+wsHpXqOUKo/bOFXzSPR9rpRxnxtfBhQl1hZonRERERERERESfi59a+eL2tEbI5WItxBKsbTGq+RjoJEk/byv0OizY9ysCX4cKsTXnAz7lVCmbkWf2gG5ubqLzWbNmIX/+/KhVq5YQs7CwgKenp8nrIyMjsWLFCqxbtw7169cHAKxfvx4+Pj44evQoGjVqZPI6lUoFlUolnEdFcW87IspaEXFqPAmJRbncTkJs9sH7ZvtLDHr0uLYf351aAxtNglF7tNIKs2v1xoYyTXBiXF1ExmuQx8UG116Eo8/qywCAUj6OojomI+oWQJlcjtjo9wIyqQSH7rxFo+LiNzN8nK1BRERERERERPS5Srm9uFQiwdWcxbC4cgeMvLBFiOcPe42Lk74HGg0HAEzZcwc1Croin5vtJ50vZQ8fdY8WtVqN9evXo2/fvqIf806ePAl3d3cUKlQIAwYMQHBwUtHkq1evQqPRoGHDhkLM29sbvr6+OH/+vNnPmjlzJhwcHIQ/Pj7pf/OaiOhjaDD/NNotOY8T6SgMn+/dK/y94Xv8dHSpycTJ4YKV0aDfEqwv2wwGiRR5XG1QyscRDtYK1Cnijp5VcqN1aW/sGlpVdF2cWoe6RTywvFcFLOpaFvM6lsIvbdK/rRcRERERERER0edG9u+v2v+r1gX+XoVEbd38D6L+Iz/hvNWic59yapSNfNTkya5duxAREYHevXsLsSZNmmDDhg04fvw4fvvtN1y+fBl169YVVo0EBQVBqVTCyclJNJaHhweCgoLMftaECRMQGRkp/Hn58uVHuSciIlNiVFocvB2EBE3S9oIh0Yl/rx26bf7vLrlOi6EX/saBVSNQ4fVdo/ZgGycMbj0BA9tMRJC9q9lxfmrliwWdy4gS1QBga5G0wFAhk6Jt2ZxwtbVIeTkRERERERER0RdD9u/vH1qZHKOaj0GswlLUPvvAQrjFhAMAolXaTz4/yh4+avJkxYoVaNKkCby9vYVYp06d0KxZM/j6+qJFixY4cOAAHj58iP3796c6lsFgMPpRMDkLCwvY29uL/hARfSojNl7D4PVXMXXPHaO2e0HRGLL+Km68jBDFi799gl3rxmD86bWw0GmMrttUsiHq91+Cg4WrAan8/WfK/7qUQcNiHuhfI2+GriMiIiIiIiIi+tyVzOkoHAc458BP9QaI2l3iozD3nwWAwfBpJ0bZykdLnjx//hxHjx5F//79U+3n5eWF3Llz49GjRwAAT09PqNVqhIeHi/oFBwfDw8PD1BBERFnmTUQ8wmLVOPEgBACw+bLxqrcbLyNw4HYQWi1OXCZqoVVj7Om12L1mNHzfGheQf+7oiS6df8GEJiMRZflhe3K2LOWNv3qWh52lcUF5IiIiIiIiIqIv2S9tfNG7ah782b0cAGBLyYY4WKiKqE/tZ1fR89o+AECcWosfd9/G2UehRmMRmfPRkierVq2Cu7s7mjVrlmq/d+/e4eXLl/Dy8gIAlCtXDgqFAkeOHBH6BAYG4vbt26hataq5YYiIPrnIeA2qzjqOstOT/r5Ka4FI2Vf3sH/VSAy/8DfkBr2oTSeRYlmF1mjUdxEu5C4FAFjQqXRmT5uIiIiIiIiI6IvmYmuBqS2Lo7GvZ2JAIsH3jUfgra2zqN/3p1YjT9hr/H78MdZeeI7uK/xMjEZkmjztLhmn1+uxatUq9OrVC3J50kfExMRg6tSpaNeuHby8vBAQEIAffvgBrq6uaNOmDQDAwcEB/fr1w5gxY+Di4gJnZ2eMHTsWJUqUQP369T/GdImI0hSn1sJamfT32fnHoei63PgfXJmZ7Im1Oh7jTq9Fr6v7IIXxktGHLrkwvuk38PcuLIq3LpMD4XFqTNtrXA+FiIiIiIiIiIgSRVjZY0zT0Vj/92QhZq1R4dd/FqCjoycglWXh7OhL9FFWnhw9ehQvXrxA3759RXGZTIZbt26hVatWKFSoEHr16oVChQrhwoULsLOzE/rNnz8frVu3RseOHVGtWjVYW1tj7969kMn4f3Ai+vSWn3mKYj8ewqE7iYXf9XqDycQJAGj1BjwOjhbFqj+7jkMrh6PP1b1GiRONVIaFVbugee+FRomT92TSjNU7ISIiIiIiIiL6WqztWxGlfRyxd3h1nM1bBmvLiHdCKv/6Hvpd3p1Fs6MvmcRgyJ5Vc6KiouDg4IDIyEgWjyei/yTP9/sBAHYWcpz9vi4azj+Ft1GqVK+pUdAVN24FYOLxFeh064jJPjc9C2B8k29w3924qHteVxsMrZ0fHcr7YP3F55i067aoPWBW6lsiEhERERERERF9bfJ8vx/W6ngcWDUCuSOChLhKpkCz3gvx2DUXJjQpgoE180GS1t7rlC1lJG/w0WqeEBFlN3aWcuy49irNxAkAWO3fiyMrhppMnCTIlZhRuw/a9PjNZOIEAE6MrY0O5X0AcOUJEREREREREVF6xSmtMLbpKOiR9HuKhU6D3/bPh0yvw8wD93HyQQji1bosnCV9CZg8ISJKJxuLtMtEucaGY9GuWfhr5y/wiAkzavfz8UWTPr/jr0rtoEvnXpsp66j80sY3fRMmIiIiIiIiIvoKXfbxxYoKrUSxUkGPMOTiVgBAn9WXUfTHg5i2905WTI++EEyeEBGl06PgGCw7/dR0o8GA1ndO4MjyoWj+4KxRc4zSCpMaDkXnLjPwzDmHySHMrRa1t1IIxw9+boxulXJneO5ERERERERERF+TX2v0wGPnnKLYyHObUTQ46bedVecCPvGs6EvC5AkRffXUWj00On26+r6JTDCKeUWFYOW2aViw7zc4JUQbtZ/MWw4N+y3G+jJNYZCY/2vXVml6ZUuDYh5oXdobPzYvBgt5+larEBERERERERF9zVQKC4xtNhq6ZL/FKPVazNs3DwqdJgtnRl8KJk+I6Kum0xtQddYx1Jh9AjEqLdovOY/FJx4L7Xq9wey1EoMe3a7/g8MrhqLu0ytG7eGWdhjd7Fv07jAVb+zd05yLnaXp5IlMKsGCzmXQt7rp+ihERERERERERGTM37sw/qzUThQrGhKA4ef/Fs4j4zTYcvkFIuOZUCGxtDfwJyLKxkKiVQiNUQMAlp1+iivPw3HleTiG1SmACTtuYdOlFyav84kIwpwDC1HlxS2T7fsKV8fUBoMQauOU7rnYWSoAEytbiIiIiIiIiIjowyys1hV1n1xG0ZAAITbk4lb8U6QaHrjlQenph2EwAIfvvMWK3hWybqL02eHKEyL6qkmT1RmJTtCK2kwlTiQGPXpe3YtDK4eZTJwE2zhhUJsfMLz19yYTJ5XzOZudS8vS3gCAHI5W6Z0+ERERERERERGZ0KCYBwBALVdgbLPR0KbYvmv2gf9BqtfB8O+mI8fuB2fFNOkzxpUnRPRViErQ4OCtIDTy9YRDsgLsyaVV9yRXeCDmHliISi9vm2z/u0R9/Fy3P6IsbQEABd1t8Sg4RmjvVN4Hs9uXRJ7v95u8fmDNfMjpZIXK+VzSc0tERERERERERGTGkm5l8SQkFpHxGng51MHS+2cx7OJWob104EP0uboXKyq0NrpWrzdAmvyNW/oqceUJEX0Vvt1yA+O338SITddFcZ0hqaaJSqsTjjstvSAcSwx69LmyG4dWDjeZOHll74YeHX/C+KajhMQJALT6dyXJex72FqnOUSGTolXpHPCwt0zfTRERERERERERkaBLRR8AQNMSnpDLpCjsaYeKeZ1hrZThf9W64IlzDlH/MWfWIWdEkHA+5+B9jPn7BqrNPo7oBNZA+doxeUJEX4Wj994CAE4/DAEAXH0ejo1+L6DVJU+eJK088XsWBgDIE/YaWzZ+jynHlsFKqzIad33pJmjcdzHO5C1r1JZyIUvJnI6i87K5ks57VsmdofshIiIiIiIiIiKxKS2KY1WfCvitQ2lRXC6TQiVX4vvGI0Rxa40KMw8uwvu9u/44+QTbr71CYGQC9t8M/FTTps8Ut+0ioq9SuyXnAQA/t/YVYipNUrZDqtehz9W9GHt6ncmkySt7d4xvMhLn85Q2+xkKedLyzsVdy6JeUXdRe6+qebB9iDcC3sUht7P1h94KEREREREREREBsFTIUKewu1FcIUv8jeayjy/WlWmKHtf/EdpqPPdHh1tHsbVkA9E1Ugm37fraMXlCRNna5ksvYKWUmW1/nKwmifrfpSL53r3CnAMLUf71PZPXrC3TDLNr9UKsReoJj/blcmLvjUDUKeyGZiW9hPiCTqVxKSAMzUt6QyKRIK+rTUZuiYiIiIiIiIiIMsBKIUONgq448ygUs2v1Rr3Hl+AdHSq0Tzq+HCfzlUeIrZMQY+6EmDwhomwrODoB3++4lWoffbKaJ2q1Gv0v7cDYM+thqVUb9X3h4IGJzUbhjE8Jo7Y6hd1w4kEIfHPYY0CNfNAbDHC3s8SBb2oY9W1dJgdal8lhFCciIiIiIiIioswnkUiwrl8lAEBQZAImvLqDVdumCe0OqlhMO7IEQ9v8IMS48oSYPCGibCsmQWsyvuv6a+H4ffIk/7uX+HbdGJR988DkNavKtcDcmj1xcmpznHgQjI1+L9CtUm6M334TLUt5Y0Gn0ngdEQ83OwtYKsyvdCEiIiIiIiIioqxjaynHifwVsLtoLbS6d0qIN314HvUe++FYgcQki0zK5MnXTmIwJHvtOhuJioqCg4MDIiMjYW9vn9XTIaIs8Cw0FnV+PZlqH5leh/6Xd+LbMxtgodMYtQc4euG7JiPhlytxtUnArGai9gSNjskSIiIiIiIiIqIvhF5vQL4f/oFzXCSOLh8C5/gooe2VvTsa9PsD8UpL1C/qgcKetuhfPR+cbJRZOGPKTBnJG0g/0ZyIiD65OLXplSfvFQh9ge3rx2HCydVGiRM9JFhZriWa9PldSJyYwsQJEREREREREdGXQ/rvipIwawecHPS9qC1nVDBGnt8MADh67y0Wn3iCSbtvf/I50ueB23YRUbag1xuEf/zeG7Dmism+Mr0OAy/twKizG2ChM06wPHXyxvim3+BKzuIfZa5ERERERERERJR1FnYujYDQOLSp2wTxlw/A6twZoa3/5Z3YWbw2HrrlAQBcCQjLollSVuPKEyL64h28HYh8P/yD5r+fEa02eROZYNS3UEgAdqwbi+9OrTFKnOghwbIKrdG0z/9EiZO6Rdw/3uSJiIiIiIiIiOiTalU6B76pXxASqRRWy/+CVp60xkCh1+Hnw39AYtADSCwcr9XpERarzqrpUhbhyhMi+qIZDAYMXn8NAHD7dRTmHnqAS8/CUCaXo6ifXKfFIL/tGHl+k8nVJk+cc2Bck1G4lrOoUVsuZ+uPMnciIiIiIiIiIspiRYrgdOu+qLvtLyFU8dVdtL91FFtLNoRUIkGf1Zdx5lEoDo2qicKedlk4WfqUuPKEiL4oBoMBIzZdx+B1V/EmIh53A6NE7avOBeDOmyisv/hCiBUKCcCO9WMx7sw6o8SJTiLFnxXbomnv/5lMnACA3mDI/BshIiIiIiIiIqLPwom2/fHc0VMU++HEKjjFRUIiAc48CgUAbPR7nhXToyzClSdE9EV5HRGPvTfeAAAO3gmCQiYx2zet2iaPnXNiXNNRuJ6jiBDrUjEXNl16IerH5AkRERERERERUfaltbDAjw2GYM3WKULMKSEa359cjZ9afyvE4tS6rJgeZRGuPCGiL0rKPIZGZzqxke/dK2xbP95kbROdRIolldqjWZ//iRInAGBvlZRTrpzPGWv7VjT6TCIiIiIiIiIiyj4MBuBUvnLYV7i6KN7p1hG0inkqnDN58nVh8oSIvihSqfmVJgAgMejR7/Iu/LN6JMoEPjBqf+iSC227z8Xs2r2hkiuN2msWdBOON/avjJqF3LjyhIiIiIiIiIgoG3v/08/0ev0RrbQStfVYPxcyfWLSJE5tvLMJZV9MnhDRF0WvN5/IyBUeiM0bJ2Dy8eWw1KpFbTqJFH9WaocWvRfghndhk9f7/VAPlgqZcP4+UaPXZ8LEiYiIiIiIiIjosxSvSUyOvLVzxW81eojaioYEoIv/QQBAcLTqk8+Nsg5rnhDRFyM4OgE15pwwiksMenS7fgATTq6CjSbBqP2pkzfGNhuNazlMF4S/NrkBHK0UkEolcLZRooinHbwdk94y4MoTIiIiIiIiIqLsKyRZUmRd2WbodPMwioYECLGxZ9ZhX9EauB+U+o4olL1w5QkRfRZCY1QIi1Ubxc8/CUXz389g29VXqPjLMaN276hgrNsyGT8fWWIycbKyXEs07fM/s4kTAHC2UQqrTBQyKQ58UwMrepUX2lNZ7EJERERERERERF84NzsL4VgnlWFa/YGidseEGIw9vQ46/kj0VWHyhIiyXIJGh/I/H0XZ6UcQp9ZiwNor2OD3HADQdZkfbr+OwtitN8QXGQzoeOMwDq0YhurPbxiN+cLBA526zMSxwRMwtnWZDM1HIpFAIkl6k6Cwp23Gb4qIiIiIiIiIiL4IE5sVRYNiHsjtYo2lPcrhYq6S2FekhqhPV/+DKP72CeuefEW4bRcRZTnR0sgLz3Hk7lscufsW3SrlNtnfPfodZh38HXWfXjHZvr50E8yo0xdxSis861cJEokEG/xe4Flo7AfNr3fVvEjQ6FGzkFvanYmIiIiIiIiI6IviYW+JZT3Li2K/1OmLeo8vwUqb+LuVFAZMOboUS040xJhGRbJimvSJceUJEX1Wkm/dZbQU0mBA6zsncGTFUJOJkzd2rujecTomNRqGOKUV9o2oLqwgOfBNDUxv7ftBc1LKpRhZryBK+zh+0PVERERERERERPRlCbR3w+IqHUSxiq/u4vniFaIXgSn7YvKEiLJUdIIG9eadEs41uqSEyerzAcKxa2w4lu78BQv2/QYHlfEKkr9L1EejfotxNm/iFl3TW/vCN4eD0G6pkCG3s/VHuAMiIiIiIiIiIspOrBQyAMCyim3xwsFD1PbDiZW4cf9VVkyLPjEmT4goS/1zKxBqrV441+mTjqfvuwsAaHr/LA6vGIZGjy4aXR9s44S+7X7E+KajEG1hI8S7Vsxl1FearI7JeyZCRERERERERET0FVvZuwLsLOVQyZWYXm+AqM0zJgxvxk9G+Z+PIuADt4inLwOTJ0SU6f6+/BKtFp9DcHRCmn2DIsXLHENjkrbtcoyPwu+7Z+OP3bPgHB9ldO2uYrXQoN8fOF6golGbTGqcFSmX2wlO1gqUyeUoxEwlVIiIiIiIiIiI6OtVJb8LbvzYEABwpEAlnM5TRtTe8ex2KN+8xMB1puvxUvbA5AkRZbrx22/ixssIzDn4wGT764h4nH8Sish4DeYffShq238rEABQ/5EfjqwYihb3zxhdH2rtgEGtf8CoFuMQaWWHSc2KYu/w6ljXLzGJUqew6cLuVkoZLv5QD9sHV0Xtf/t0q2S8QoWIiIiIiIiIiL5u0vcv5kokmFZ/ILSSpJ/SLbVqjDu1Fg/fxmTR7OhTkGf1BIgo+3oXY7p4VrVZxwEAVfO7GLXZJ8RgyrG/0O72cZPX/lOoKiY1GoYw68R6Jk18PdG/Rj6h/eqk+nC0Vpqdk4U8cc/KxV3L4uLTd6he0DV9N0NERERERERERF+lJy4+2FCmCXpd2y/E2tw9iVXlW0Knbwr/l+HwzeEAvR64GxiFMj6OSckX+mIxeUJEmeLYvbe49CwM4xsXEWJavcGoX1Bk0lZe55+8E7XVfHoVsw/8D14x71JehghLW/zYYAj2FK0pFCoJmNXMqJ+LrUW65mtjIUe9oh5pdyQiIiIiIiIioq/ewmpd0fn+KVjEJa02mXh8BUpOKYJYjR4tS3kjJFqFC0/f4Zc2vuhWKXcWzpYyA5MnRJQp+q1J3OOxiJedENOZSJ7MPHDPKGatjscPJ1aiu/8Bk2MfzV8BExqPQIitcybNloiIiIiIiIiIKHUHR9WA39MwvI6Ih4uNEvEu38Fi6mShvdKrO6h+5ywOFaqKPTfeCPG/L79k8iQbYPKEiP4zfbIkSfIC8AYD8OJdHHqu9EO/GvnQo3Ju7PZ/I7q27Kt7mLd/HvJEBBqNG6W0xk/1B2Kbbz1htQkREREREREREdGnUMTTHkU87YXzMN+ReDXvd+SMChZi359cheP5K0AjUwix1LaUpy8HC8YT0X+24dIL4Vir0wvHFgoppu29g4B3cZi867boGqVWg/GnVmPrxu9MJk5O5ymDRv0WY1uJ+kycEBERERERERFRlrO2t8Gs2r1Fsbzhgehx7R9RzMlaAfryMXlCRP/ZhovPheM4jU44vh8YjWP3kzLxPVdegrudBYoEP8PutaMx9OI2yAx60VhxCgtMajgUPTv+hEB7N7OfefTbWpl4B0RERERERERERKmzkEuxr0gNXPMuLIqPPL8JDvHRwrmVUvapp0YfAZMnRPSfSZOtDIlXJyVPgqISRP3O3g9C2yMbsGfNaBQNCTAa50qOomjS53esL9M0zdUmBdxt/9ukiYiIiIiIiIiIMkAikeDQ6Fo4MeA7UdwxIQZDLm5N3vPTTow+CiZPiOg/S57niFVpTfbJFR6Ivzd+j+9PrYZSL+6jkclxbeh36Nh1Fp47eRtdWzW/S6bOl4iIiIiIiIiI6EMU9rRD+xEdsa9wdVG897V98IgOBcAd6LMLJk+IKMPUWj2iEjTCefJ/EJJv2wUAMBjQ7fo/OLBqBMq/vmc01j23POgx6Hc87z8ceqnpJY3Le5XPlHkTERERERERERH9VzYWcsyt1ROaZL9lWWrV+ObcZgBcd5JdZHryZOrUqZBIJKI/np6eQrvBYMDUqVPh7e0NKysr1K5dG3fu3BGNoVKpMGLECLi6usLGxgYtW7bEq1evMnuqRPSBGi04jZJTDyMsVg0AkCT7JyEu2coT9+h3WL11Kn45/AdsNOItvHQSKf6o3B6tes7HfY98aFbCG42Ke2Bo7fwYVCsfdg2rhvvTG+Pm1IawVsqF61qV9sbpcXU+8h0SERERERERERGZZqOU47mTN7aUbCiKd7x5GHnDXkMiSXz5WK83ZNEMKTPI0+6SccWLF8fRo0eFc5ksKQM3EFXVAwAANrVJREFUZ84czJs3D6tXr0ahQoXw888/o0GDBnjw4AHs7OwAAKNGjcLevXuxefNmuLi4YMyYMWjevDmuXr0qGouIPj2DwYBnobEAgPNPQmFnqcCt15FC+4kHIQCAFndPYfqRJXBMiDEaI8DRC2OajcbVnMUAAMOr5YVSLsXSHsYrTCwV4v/mK+V1QS4X60y7HyIiIiIiIiIiooywUsrQvlxO3PP5BvGjjsNKqwIAyA16jDmzHqcaVEKVmceQz80GWwdXzeLZ0of6KMkTuVwuWm3ynsFgwIIFCzBx4kS0bdsWALBmzRp4eHhg48aNGDRoECIjI7FixQqsW7cO9evXBwCsX78ePj4+OHr0KBo1avQxpkxEAFRaHc4/fodK+ZxFqz2SW3H2mXA8fON1o3aH+Gj8fPgPtLh/xuT160s3wYw6fRGntAIAbB1cBWV8HNM9xxxOVunuS0RERERERERE9DH82qEUgFJ4cXMQcv31PyHe/P4Z7D13Ee8sc+Ldv7u20Jfpo9Q8efToEby9vZE3b1507twZT58+BQA8e/YMQUFBaNgwaTmThYUFatWqhfPnzwMArl69Co1GI+rj7e0NX19foY8pKpUKUVFRoj9ElDG/7L+HPqsv45vN/mb7zPjHuG7Je7WeXsXhlcNMJk7e2jqjd/upmNRomJA4AYAKeZwhl6X9V9HavhXxfZMiqFnQNc2+REREREREREREn8Kd7oMQaWEjivX7Z7lwbDBw664vVaYnTypVqoS1a9fi0KFDWLZsGYKCglC1alW8e/cOQUFBAAAPDw/RNR4eHkJbUFAQlEolnJyczPYxZebMmXBwcBD++Pj4ZPKdEWV/ay88BwAcufvWZLtOb4CprRqt1fH45dAirNk6BR4xYUbte4rWRMO+i3Eyv3hbroWdS6d7bjULuWFwrfyQSFhyi4iIiIiIiIiIPg+Fi+TCn5Xbi2IVH11Blec3ACT+nkZfpkxPnjRp0gTt2rVDiRIlUL9+fezfvx9A4vZc76X88dNgMKT5g2hafSZMmIDIyEjhz8uXL//DXRCRKSHRKqNYuVd3cWDVCHTzP2jUFmFpixEtxmH/hN/Qo2kZId64uCfu/dQYrUrn+KjzJSIiIiIiIiIi+pjyudmi5OzJeGvrLIp/d2oNYDBAo2Py5Ev1UWqeJGdjY4MSJUrg0aNHaN26NYDE1SVeXl5Cn+DgYGE1iqenJ9RqNcLDw0WrT4KDg1G1qvniOhYWFrCwsPg4N0H0lZBKYHJlycWn77Ds9FNULZC0ZZZSq8Hosxsw8NIOyAx6o2tO5i2H8U1GItjOBaebFkMuF2sMqJkP0QkaeNhbQpGOrbqIiIiIiIiIiIg+d2WL5sD/qnbGL4f/EGKlAx+i/uNLUOsawQqyLJwdfaiP/uulSqXCvXv34OXlhbx588LT0xNHjhwR2tVqNU6dOiUkRsqVKweFQiHqExgYiNu3b6eaPCGi/05qZnVXz5WXcOx+MKbvuwsAKBr8FLvXjsYQv21GiZM4hQV+aDQMvTtMRbCdCwBALksc18FKgZxO1kycEBERERERERFRtmGpkGFLyYZ45uQlin9zbiO2XXkJrc74xWP6/GX6L5hjx47FqVOn8OzZM/j5+aF9+/aIiopCr169IJFIMGrUKMyYMQM7d+7E7du30bt3b1hbW6Nr164AAAcHB/Tr1w9jxozBsWPHcP36dXTv3l3YBoyIPh5zO+OptYl/wUv1Ogy5uBW713yLoiEBRv2u5CiKJn1+x8bSTUSDvU+eEBERERERERERZTdWChm0MjkWVusqipd4+wQXFqzGmn/rDNOXJdO37Xr16hW6dOmC0NBQuLm5oXLlyrh48SJy584NABg/fjzi4+MxdOhQhIeHo1KlSjh8+DDs7OyEMebPnw+5XI6OHTsiPj4e9erVw+rVqyGTcXkT0cei0elFezCO3XoD266+QvtyOQEAucIDMW//PJR/fc/oWrVUjnk1uuOvim2glyb+d9qshBf23woEACikXGlCRERERERERETZk1Ke+NvX3qI1MeL8ZuQPey20jTq3EXOaNkO/6nmzanr0gSQGgyFbVqyJioqCg4MDIiMjYW9vn9XTIfqsGQwG5J3wj7lGdLp5GD8eWwYbTYJR8z23PBjdfAzuuyf9A1AxjzN+al0cjRecAQDcmtoQdpaKjzJ3IiIiIiIiIiKirJbn+/0AgNZ3TmDBvt9EbVP7z0Bco6a4FxiNXzuUQmFPO1ND0CeQkbwBXwcn+krcD4pCr5WXcOtVpFHbvcBok9e4xEZg2Y6fMfvg70aJE51EisWVO6BVz/mixAkA/D24CjzsLIVz1jghIiIiIiIiIqKvwd6iNfHEOYco1n7vCvx9+SVuvY7EoHVXsmhmlFH8RZPoK9FjxSWcehiCNn+cAwDMPngfteeewIUn79B39WWj/nU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      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(k), AC_1D_Yeh)\n",
    "plt.plot(range(k), ac_1d_yeh*slope, color='red', lw=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
